explain xkcd - User contributions [en]

Talk:3143: Question Mark

2025-09-18T04:11:26Z

Vandof: /* Instances in Media */ new section

Surely it should read CharlieApostraphe’s Angels, right? [[User:KelOfTheStars!|KelOfTheStars!]] ([[User talk:KelOfTheStars!|talk]]) 02:30, 18 September 2025 (UTC)
:You apostrophe re almast right period. tilde tilde tilde tilde [[Special:Contributions/2607:FB91:7914:D333:3D03:FB75:B160:75F4|2607:FB91:7914:D333:3D03:FB75:B160:75F4]] 03:08, 18 September 2025 (UTC)
::You still have to put the punctuation mark after the word open parenthesis (in this case comma, the apostrophe end parenthesis) btw period. tilde tilde tilde tilde [[User:TheTrainsKid|TheTrainsKid]] ([[User talk:TheTrainsKid|talk]]) 03:20, 18 September 2025 (UTC)
Someone should do a grammar tag or whatever comma, like the citation needed tag comma, that links to this comic period. tilde tilde tilde tilde [[User:TheTrainsKid|TheTrainsKid]] ([[User talk:TheTrainsKid|talk]]) 03:20, 18 September 2025 (UTC)

== Instances in Media ==

In the Amazing World of Gumball episode "The Line", Gumball refers to "Stellar Odyssey Colon The Force Rehashed". [[User:Vandof|Vandof]] ([[User talk:Vandof|talk]]) 04:11, 18 September 2025 (UTC)

3125: Snake-in-the-Box Problem

2025-09-17T04:59:20Z

Vandof: Added trivia section

{{comic
| number = 3125
| date = August 6, 2025
| title = Snake-in-the-Box Problem
| image = snake_in_the_box_problem_2x.png
| imagesize = 359x611px
| noexpand = true
| titletext = Chemistry grad students have been spotted trying to lure campus squirrels into laundry hampers in the hope that it sparks inspiration.
}}

==Explanation==
This comic makes fun of the fact that many fields of math and science use analogies to help visualize complex problems. One such analogy, drawn in the comic, involves a snake on the edges of an n-dimensional hypercube, which is a real problem in graph theory called {{w|snake-in-the-box}}. In this problem, a snake is coiled around the edges of an ''n''-dimensional hypercube. No two adjacent corners of the cube can be occupied by non-consecutive parts of the snake (i.e., the snake can't come near itself). The problem involves finding the longest snake for a box of a given dimension. This problem has been solved up to an 8-dimensional cube, but remains unsolved for 9 dimensions and up. (The proper name for this problem, as stated in [https://oeis.org/A099155 OEIS A099155], is "Maximum length of a simple path with no chords in the n-dimensional hypercube" but, as the entry acknowledges, "snake-in-the-box problem" is the name commonly used for it.) Because a common way to formulate hypercubes is as a graph of N-tuples (each corner has N coordinates, each a 0 or 1 - for example, a {{w|Square|2-cube}} has vertices (0,0), (0,1), (1,0), (1,1) - and edges are drawn between vertices differing only in one coordinate), and this problem in particular pertains to connecting edges between vertices, this comic considers the problem to be an example of this phenomenon for the mathematical field of graph theory.

The other thought experiment alluded to is {{w|Schrödinger's cat}}, which is used in quantum physics. In this thought experiment, a cat is put in a box which contains poison, a radioactive source and a {{w|Geiger counter}}. This aims to illustrate an apparent paradox in the principle of {{w|quantum superposition}} — a property of quantum mechanics in which objects can exist in two apparently incompatible states simultaneously, so long as no attempt is made to verify which state they are in. If an atom of the radioactive source decays, the poison is released, and the cat dies, tying its fate to the radioactive decay. Since radioactive decay obeys quantum mechanics, so long as the particle is not observed it will exist in a superposition of two states: decayed and not decayed. Therefore, the cat, too, may be considered to exist in a superposition of two states (alive and not alive) which appears to be absurd. The opening of the box collapses the superposition so that only one of those states remains.

The comic jokes that these two "cute animal in a box" thought experiments are instances of a universal rule that applies to every field of study. Other fields have simply yet to "discover" their own analogies. Whether a snake counts as a "cute animal", that would satisfy the "rule" is likely to occasion some debate.

The title text takes this further by claiming that chemistry students have been trying to fix the lack of cute-animal-in-box thought experiments in their field by attempting to trap a squirrel with a laundry basket. This is possibly a reference to {{w|Endohedral fullerene}} complexes, where an ion or atom is caged inside a spherical structure of carbon. Those students seem to hope that it will inspire them in some way, maybe similarly to what is depicted in [[1584: Moments of Inspiration]].

==Trivia==
The comic number 3125, being equal to 55, is itself representable in terms of a (5-dimensional) box.

==Transcript==
:[A panel with text both above and below the illustration, with further text outside the panel below.]
:[In the panel, above the illustration:]
:A snake slithers around a hypercube. No two non-consecutive parts of its coils can be on adjacent corners.
:[Three small illustrations of 4-dimensional hypercubes, each with a snake slithering around its edges. Each illustration has a red line or lines indicating an edge or edges where two non-consecutive parts of the snake are on adjacent corners. Below each hypercube is a red X.]
:[A large illustration depicting a 4-dimensional hypercube with a snake slithering around its edges.]
:[Below the large illustration is text printed in green. To the left of the text is a green checkmark.]
:Dimensions=4
:Max length=7
:[The following text is printed in black, except for the last word "UNSOLVED" which is printed in red:]
:Snake(N) = Largest snake that can fit in an N-dimensional hypercube
:Snake(N=1, 2, 3 .. 8) = 1, 2, 4, 7, 13, 26, 50, 98
:Snake(N>8) = UNSOLVED

:[Text outside the panel:]
:It turns out every scientific field has a key thought experiment that involves putting a cute animal in a weird box for no reason.
:So far, quantum mechanics and graph theory have found theirs, but most other fields are still working on it.

{{comic discussion}}<noinclude>

[[Category:Comics with color]]
[[Category:Math]]
[[Category:Physics]]
[[Category:Animals]]
[[Category:Cats]]
[[Category:Squirrels]]

2200: Unreachable State

2025-01-24T04:48:57Z

Vandof: Corrected "September 09" to "September 9"

{{comic
| number = 2200
| date = September 9, 2019
| title = Unreachable State
| image = unreachable_state.png
| titletext = ERROR: We've reached an unreachable state. Anything is possible. The limits were in our heads all along. Follow your dreams.
}}

==Explanation==

When writing a computer program, developers often need to make assumptions about what state the system could potentially be in at the time the program is executed. For example, a program designed to fetch data from a database requires that the database be accessible at the time it tries to fetch data; if it is not, then the program needs to know how to handle that state, or it might simply hang or crash the system. A good developer will have accounted for this possibility and may give the program a way to fail gracefully; often, this is done by outputting an {{w|error message}} to the user, to tell them what is wrong.

Sometimes, cautious developers will identify states that, in theory, should never be reachable ''at all'' - if they were, it would imply that something has gone fundamentally wrong. A paranoid developer might still decide to handle this case anyway, perhaps including a note that the situation should ''theoretically'' never happen, but they aren't confident enough to state with absolute certainty that it cannot.

This comic shows [[Cueball]] reading (or possibly writing) just such an error message from a program he is using. The developer has evidently written this text while tired (possibly from sleep deprivation), and did not trust themself enough to be sure that the state is truly unreachable. The hopeless tone of the message supports this lack of confidence in their work.

The title text refers to the common trope of a character being given a "magic" item and winning something because of it, then being told that the item was not actually magic and that the magic was {{tvtropes|MagicFeather|inside them all along}}. It is often used as a fable to tell people to follow their dreams. The title text puts the fable in a place where it doesn't belong, saying that finding the "unreachable state" that is the error code implies that the finder can do anything.

==Transcript==
:[Cueball, sitting on an office chair at his desk with his hands over his laptop computer. There is an error message on the screen which is displayed above him with a zigzag line from the screen to the text. The exclamation mark at the top is shown in white on a black triangle.]
:! Error
:If you're seeing this, the code is in what I thought was an unreachable state.
:I could give you advice for what to do. But honestly, why should you trust me? I clearly screwed this up. I'm writing a message that should never appear, yet I know it will probably appear someday.
:On a deep level, I know I'm not up to this task. I'm so sorry.

:[Caption below the panel:]
:Never write error messages tired.

{{comic discussion}}

[[Category:Comics featuring Cueball]]
[[Category:Programming]]

2179: NWS Warnings

2025-01-24T03:47:36Z

Vandof: /* Explanation */ Corrected parentheses to brackets

{{comic
| number = 2179
| date = July 22, 2019 
| title = NWS Warnings
| image = nws_warnings.png
| titletext = Kind of rude of them to simultaneously issue an EVACUATION - IMMEDIATE alert, a SHELTER IN PLACE alert, and a 911 TELEPHONE OUTAGE alert.
}}

==Explanation==

The {{w|National Weather Service}} (NWS) is a United States federal agency that is tasked with issuing national weather forecasts and {{w|Severe weather terminology (United States)|extreme weather alert}}s.

This comic portrays the NWS as a person that needs breaks, which is absurd, as it is an important service and would probably always have staff active, even on holidays. For example, the NWS [https://www.washingtonpost.com/news/capital-weather-gang/wp/2013/10/04/weather-service-office-begs-please-pay-us-in-secret-message/ continued to work during federal government shutdowns], as it was considered an essential service for the protection of life and property. Even if one of the NWS's 122 local weather offices were to be incapacitated, contingency plans are in place to ensure that nearby offices act as emergency cover; as happened in March 2019 with [https://twitter.com/mikeseidel/status/1106705454435057666 flooding in Nebraska forcing the NWS office in Valley to evacuate.]

Regardless, in this comic the NWS has decided to take a break, and so has opted to issue every extreme weather alert possible for the entire contiguous portion of the United States (including DC, but not Alaska or Hawaii) to make sure no one is caught by surprise by extreme weather, since the NWS will not be able to issue warnings. As the NWS could not be sure which areas will need to get warned of severe incidents, the NWS has decided to issue warning polygons that cover the entire United States (ostensibly except Alaska and Hawaii). A layer of humor is that this would necessitate warnings where they would be highly unlikely to occur in real life; examples include issuing blizzard warnings for Florida, where any amount of snow is rare, and tsunami warnings for areas very far from any ocean coastline. The large quantity of implausible warnings would also most likely cause people to ignore all of them, defeating the purpose of issuing the warnings in the first place.

Each of the text warnings within the map are coloured, which matches the [https://www.weather.gov/bro/mapcolors NWS color coding] used for a given warning event.

The title text mentions how some of the warnings that have been issued require action to get to safety that contradicts the other warnings, for example, an evacuation warning and a shelter in place order, since doing one would mean failing to do the other. This confusing scenario would likely prompt many concerned citizens to call emergency services for clarification, but the 911 outage alert would advise against this, adding another layer to the absurdity of the occurrence of the NWS taking a break. A similar contradiction is present in [[2841: Sign Combo]].

This comic was likely inspired by the heat wave that impacted two-thirds of the US for more than a week.

NWS and tornado warnings was later mentioned in the title text of [[2219: Earthquake Early Warnings]].

=== Table of warnings ===
Assumptions about text outside of the frame are given in square brackets. [https://www.weather.gov/help-map This page from the NWS] lists all the warnings and colors, including all the hex codes for them which we <s>stole</s> referenced.
{| class="wikitable"
!Warning
!Color
!Explanation
|-
|'''Gale warning'''
|Plum
|In the United States, the National Weather Service issues gale warnings for marine areas (oceans, sounds, estuaries, and the Great Lakes) experiencing, or about to experience, winds within the range of 34 knots (63 km/h; 39 mph) to 47 knots (87 km/h; 54 mph). Listed twice.
|-
|'''Tornado Warning'''
|Red
|A {{w|tornado}} warning is issued for an area if a tornado is radar indicated, radar confirmed, or members of the public confirm the existence of a funnel cloud or a tornado. As tornadoes are more apt to form in different parts of the country at different times a country-wide tornado warning would be highly unlikely. There ''is'', however, one past instance of a ''statewide'' tornado warning according to the ''[https://web.archive.org/web/20190406193904/https://www.farmersalmanac.com/super-tornado-outbreak-10903 Farmers' Almanac]'' – during the {{w|1974 Super Outbreak}}, forecasters were supposedly so overwhelmed by the sheer number of tornadic storms that they issued a single tornado warning covering the entire state of Indiana.
|-
|'''Flash Flood warning'''
|Dark red
|Flash flooding is occurring, imminent, or highly likely. A flash flood is a flood that occurs within six hours of excessive rainfall and that poses a threat to life and/or property. Ice jams and dam failures can also cause flash floods.
|-
|'''Air Quality''' [Alert]
|Gray
|An air quality alert informs the public about pollution levels in the air and advises vulnerable groups such as children and people with lung disease to take precautions.
|-
|'''Frost Advisory'''
|Cornflower blue
|Minimum sheltered temperatures are forecast to be 33 to 36 °F (1 to 2 °C) during the locally defined growing season on nights with good radiational cooling conditions (e.g., light winds and clear skies). Widespread frost can be expected. Listed twice.
|-
|'''Severe Thunderstorm Warning'''
|Orange
|A severe thunderstorm is indicated by Doppler weather radar or sighted by Skywarn spotters or other persons, such as local law enforcement. A severe thunderstorm contains large damaging hail of 1 inch (2.5 cm) in diameter or larger, and/or damaging winds of 58 mph (93 km/h) or greater. These warnings are currently issued on a polygonal basis.
|-
|'''Dense Fog Advisory'''
|Slate gray
|Widespread or localized fog reducing visibilities to 1⁄4 mi (0.4 km) or less.
|-
|[Hurricane Force W]'''ind Watch'''
|Western red
|A hurricane force wind watch is issued by the National Weather Service of the United States when the risk of sustained winds or frequent gusts of 64 knots (118 km/h, 74 mph) or greater are predicted to occur. The winds must not be directly associated with a tropical cyclone, or a hurricane warning will be issued.
|-
|'''Tropical Storm Warning'''
|Firebrick
|A warning that sustained winds within the range of 34 to 63 kn (39 to 73 mph or 63 to 117 km/h) associated with a tropical cyclone are expected in a specified area within 36 hours or less.
|-
|'''Ice Stor'''[m Warning]
|Dark Magenta
|Heavy ice accumulations are imminent. The criteria for amounts vary over different county warning areas. Accumulations range from 1⁄4 to 1⁄2 inch (6.4 to 12.7 mm) or more of freezing rain. Listed twice.
|-
|[Extreme Cold]''' Warning'''
|Blue
|The NWS does not issue cold warnings. As the text is cut off, Randall probably means Extreme Cold Warning, which the NWS offices in Alaska issue. This implies that the entire U.S. will get colder. This does not make sense, partly because in the time this comic was released, it was summer in the U.S., but also because Alaska, the one state that does receive this type of warning, is not shown.
|-
|'''Heat A'''[dvisory]
|Coral
|High Heat Index (HI) values are forecast to meet or exceed locally defined warning criteria for one or two days. Typical HI values are maximum daytime temperatures above 100 to 105 °F (38 to 41 °C) and minimum nighttime temperatures above 75 °F (24 °C).
|-
|[Flood]''' Advisory'''
|Spring green
|For nuisance type flooding meeting one of the following criteria: <3 feet of standing water, enough to cause minor flooding of roads, especially in poor drainage locations; <6 inches of fast flowing water across roads; or Arroyos/streams/creeks nearing bankfull, or briefly overtopping banks, producing < 6 inches of fast flowing water.
|-
|'''Snow '''[Squall Warning]
|Medium violet red
|Snow squall warning is a bulletin issued by he National Weather Service in the United States to warn population of two types of snow events reducing visibility in blowing snow: Lake effect snow squalls and Frontal snow squalls. Criteria for the National Weather Service to issue a Snow squall warning: Visibility of less than one quarter of a mile, sub-freezing temperatures on the ground, expected to last in one area less than 60 minutes, and may cause dangerous and life-threatening conditions.
|-
|[Storm Surge]''' Warning'''
|SSWarning
|Localized heavy flooding due to storm surge caused by a tropical cyclone is occurring or is imminent in the next 12 hours, which poses a threat to life and/or property.
|-
|'''Brisk W'''[ind Advisory]
|Thistle
|A Small Craft Advisory issued by the National Weather Service for ice-covered waters.
|-
|[Lake Effect Snow]''' Watch'''
|Light sky blue
|Significant amounts of lake-effect snow (generally 6 inches within 12 hours or 8 inches within 24 hours) are possible in the next 12 to 48 hours.
|-
|'''Coastal Fl'''[ood Advisory]
|Lawn green
|Minor coastal flooding is occurring or is imminent in the next 12 hours, which poses a threat to life and/or property.
|-
|'''Dense Smo'''[ke Advisory]
|Khaki
|Widespread or localized smoke reducing visibilities to 1⁄4 mi (0.4 km) or less.
|-
|[Severe Weather Sta]'''tement'''
|Aqua
|A National Weather Service product which provides follow up information on severe weather conditions (severe thunderstorm or tornadoes) which have occurred or are currently occurring.
|-
|[Lakeshore Flood]''' Advisory'''
|Lawn green
|Minor lakeshore flooding is occurring or is imminent in the next 12 hours, which poses a threat to life and/or property.
|-
|'''Wind Chill Ad'''[visory]
|Pale turquoise
|Dangerous wind chills making it feel very cold are imminent or occurring; the criteria varies significantly over different county warning areas.
|-
|'''Blizzard Warn'''[ing]
|Orange red
|Sustained winds or frequent gusts of 35 miles per hour (56 km/h) or greater, considerable falling, and/or blowing snow reducing visibility frequently to 1⁄4 mile (0.40 km) or less for a period of three hours or more. There are no temperature criteria in the definition of a blizzard, but freezing temperatures of at least 0 °C (32 °F) and 35 miles per hour (56 km/h) winds will create wind chills of at least −8.5 °C (16.7 °F).
|-
|'''Hurricane Warning'''
|Crimson
|A warning that sustained winds 64 kn (74 mph or 118 km/h) or higher associated with a hurricane are expected, and tropical storm conditions are expected within 36 hours in a specified area. A hurricane warning can remain in effect when dangerously high water or a combination of dangerously high water and exceptionally high waves continue, even though winds may be less than hurricane force (also automatically indicates a Tropical Storm Warning).
|-
|'''Extreme Fire '''[Danger]
|Dark salmon
|Fires start quickly, spread furiously, and burn intensely. All fires are potentially serious.
|-
|[Freezing Fog Adv]'''isory'''
|Teal
|Widespread dense fog reducing visibility to less than 1⁄4 mile (400 m) that occurs in a sub-zero environment, leaving a thin glazing of ice.
|-
|'''Tsunami Warning'''
|Tomato
|Warnings are issued due to the imminent threat of a tsunami from a large undersea earthquake or following confirmation that a potentially destructive tsunami is underway. They may initially be based only on seismic information as a means of providing the earliest possible alert.
|-
|'''Avalanche W'''[arning]
|Dodger blue
|A warning of current or imminent avalanche activity when avalanche danger is considered high or extreme. Authorized officials may recommend or order protective actions according to state law or local ordinance when natural or human-triggered avalanches are likely to affect roadways, structures, or backcountry activities.
|-
|'''Fire Warning'''
|Sienna
|A fire is currently burning in the area and evacuation is recommended.
|-
|'''Volcano Warn'''[ing]
|Dark slate gray
|A warning of current or imminent volcanic activity. Authorized officials may recommend or order protective actions according to state law or local ordinance.
|-
|'''Ashfall Advisory'''
|Dim gray
| Airborne ash plume resulting in an ongoing deposition at the surface. Ashfall may originate directly from a volcanic eruption or from the re-suspension (by wind) of a significant amount of relic ash.
|-
|'''Red Flag Warning'''
|Deep pink
|A red flag warning means that conditions are favorable for the rapid spread of wildfires. While there are very few areas immune to wildfires, one that encompasses the entire country would be unlikely unless a conflagration of epic magnitude swept through the country.
|-
|'''Radiological hazard warning'''
|Indigo
|A radiological hazard warning is a non-weather event that is transmitted by the NWS. This means that a radiological source was lost, discovered, or released accidentally or maliciously. If the entire country were under such a warning, the outlook for the citizens would be pretty grim.
|-
|'''Evacuation - Immediate'''
|Chartreuse
|Evacuation Immediate is a warning issued through the Emergency Alert System (EAS) in the United States to notify the public of a mandatory evacuation due to a wildfire, approaching hurricane, or an imminent explosion due to a gas leak.
|-
|'''Shelter In Place Warning'''
|Salmon
|Shelter In-Place Warning is to seek safety within the building one already occupies, rather than to evacuate the area or seek a community emergency shelter. The American Red Cross says the warning is issued when "chemical, biological, or radiological contaminants may be released accidentally or intentionally into the environment" and residents should "select a small, interior room, with no or few windows, taking refuge there."
|-
|'''911 Telephone Outage'''
|Silver
|An emergency message that defines a local or state 911 telephone network outage by geographic area or telephone exchange. Authorized officials may provide alternative phone numbers in which to reach 911 or dispatch personnel.
|}

==Transcript==
[Heading on top of frame:]

Alert: Everyone Just Keep An Eye Out In General

[A map of the 48 contiguous states of the United States, surrounded by several warning polygons that cover most or all of the area, along with parts of neighboring countries or the sea.]

[The following warning headers are printed in different colors around the map of the United States, some of which are cut off by the frame. Assumptions about text outside of the frame are given in square brackets.]

Gale Warning, Tornado Warning, Flash Flood Warning, Air Quality [Alert] 
Frost Advisory, Severe Thunderstorm Warning, Dense Fog Advisory 
[Hurricane Force W]ind Watch, Tropical Storm Warning, Ice Stor[m Warning] 
[Extreme Cold] Warning, Heat A[dvisory] 
[Flood] Advisory, Snow [Squall Warning] 
[Storm Surge] Warning, Brisk W[ind Advisory] 
[Lake Effect Snow] Watch, Coastal Fl[ood Advisory] 
Dense Smo[ke Advisory] 
[Severe Weather Sta]tement, Gale War[ning] 
[Lakeshore Flood] Advisory, Wind Chill Ad[visory] 
[Extreme] Cold Warning, Blizzard Warn[ing] 
Hurricane Warning, Extreme Fire [Danger] 
[Freezing Fog Adv]isory, Tsunami Warning, Avalanche W[arning] 
[Ice S]torm Warning, Frost Advisory, Fire Warning, Volcano Warn[ing] 
Ashfall Advisory, Red Flag Warning, Radiological Hazard Warning 

[Text below frame:]

When the National Weather Service needs to take a day off, they just issue warnings for everything so no one is caught by surprise.

{{comic discussion}}

[[Category:Comics with color]]
[[Category:US maps]]
[[Category:Weather]]
[[Category:Tornadoes]]
[[Category:Geology]]
[[Category:Volcanoes]]

284: Tape Measure

2025-01-23T09:27:57Z

Vandof: Fixed "threshhold" -> "threshold"

{{comic
| number = 284
| date = July 2, 2007
| title = Tape Measure
| image = tape_measure.png
| titletext = This sequence was later reproduced in the International Tape-Extending Federation archives, retitled 'The Founding of the Sport'.
}}

==Explanation==
[[Cueball]] acts childishly, finding a tape measure and then playing with it. He then extends it to 8 feet (approx. 2.5 meters), wondering whether or not that was a record, which makes him imagine a sport where extending the tape measure as far as possible was the goal.

{{w|Tape measure}} strips, of the 'spring metal' kind are manufactured with a slight inherent curve upwards, laterally, where not curved along their length (e.g. whilst still on the spool). Extending the tape straight out from the spool, the sideways curve dominates and adds structural strength to ''keep'' the relatively light tape-strip supported against gravity. By doing so, it allows fairly easy operation to extend a tape upwards (e.g. from the floor to the ceiling of a room) or for a smaller distance sideways (e.g. the width of a picture-window) without needing a second person or the extra effort of hooking the 'end hook' over something at the 'end-point' before pulling the case back fowards the 'start'. The tape can also still be bent around corners or circumferences, at the loss of local longitudinal strength and perhaps some accuracy, if a single straight-line distance isn't desired. It is this combination of flexibility and rigidity that makes such tapes so useful for common household and maintenance measurements larger than a piece of paper (for which a rigid ruler is more useful) but smaller than a property's yard area (where a surveyor's non-sprung metal tape might be laid out) and not habitually involving curves (as with a draper's cloth tape).

However, as a tape measure is extended (especially horizontally), the weight of the strip eventually does overcome the support offered by the bend, causing it to collapse. As cleverly depicted in the comic, a single point tends to 'crumple' (often where vibrations from the handling induce a resonance; and tending towards where the cantilever forces are greatest, near where the operator is currently drawing the tape out) and this then causes a collapse in which other bends introduce themselves from the dynamics of the tape in motion and the force of its impact on the ground/other objects.

Skillfully and steadily holding the tape measure at an angle can redirect some of the weight load, reduce the momentary tendencies to cross the 'bending threshold' and allow for a longer total extension. Vertically, it is likely that most such tape can support itself (with minimal care) against collapse, but would reach no length at all in a sideways direction. The ultimate aim of those who attempt idle 'tape extending' challenges is often to achieve the longest ''horizontal'' extension. Or the highest 'figure' revealed from the tape, whilst doing so, which would actually be the length of the slightly arced diagonal, but would be fairly close to the slightly smaller 'reach length' attained, and usually good enough for idle entertainment. However, it is implied that this technique can be explored to the point of becoming its own sport, at which point one presumes that professional "competitive tape extension" would rely solely upon the observed horizontal extension (without, or prior to, hitting the ground), with competitor's chosen extension techniques with their standard (competition-grade) tapes perhaps even making on-tape graduations unnecessary and totally irrelevent.

The title text refers to a future where this sport exists, and this comic is a representation of the origin of this sport.

==Transcript==
:[Cueball finds a tape measure.]
:Cueball: Hey, a tape measure.

:[Cueball extends the tape measure.]
:''extend extend''

:[The tape measure falls.]
:''clatter''

:[Cueball tries again.]
:''click''
:''schwoop''

:''extend extend''

:''extend''

:Cueball (thinking): Ooh, eight feet. I wonder if that's a record.

:[Cueball imagines an olympic stadium, with three people extending tape measures]
:Audience: ''Gooo! Goooo! Gooooooo!''

==Trivia==
*During the real-life meet-up at the time & place mentioned in [[240: Dream Girl]], fans [https://web.archive.org/web/20160605010651/http://thephoenix.com/boston/news/48208-wisdom-of-crowds/ participated in a tape-measure length competition].

{{comic discussion}}
[[Category:Comics featuring Cueball]]

Talk:3015: D&D Combinatorics

2024-12-05T13:31:22Z

Vandof: Added comment

The bot originally created this page as “D Combinatorics”. I renamed it to the correct title and tried to get as many of the references as possible (including a few redirects). [[User:JBYoshi|JBYoshi]] ([[User talk:JBYoshi|talk]]) 00:54, 23 November 2024 (UTC)

:The title in the Atom feed (which I'm assuming the bot consumes) is "D Combinatorics". I'm guessing something in Randall's pipeline didn't like the ampersand. --[[Special:Contributions/162.158.154.160|162.158.154.160]] 01:41, 23 November 2024 (UTC)

::Yup, if you look at [https://xkcd.com/3015/info.0.json 3015's JSON] you see that <code>title</code> and <code>safe_title</code> differ, and if you look at the HTML page source you'll see '''3''' different things: <code><title>xkcd: D Combinatorics</title></code>, <code><meta property="og:title" content="D&amp;D Combinatorics"></code>, and <code><div id="ctitle">D&D Combinatorics</div></code>! So probably what happened is Randall entered D&D but was supposed to enter D&amp;D, and the openGraph tags adder code, having to be HTML-aware, decoded & normalized D&D as HTML would, but the other parts of the pipeline just ate it for some reason. {{unsigned ip|172.69.65.224|06:09, 23 November 2024}}

::: The problem now is that the feed doesn't validate (because it contains a bare &) and it's also not updating (maybe because of the previous problem). --[[Special:Contributions/172.71.119.13|172.71.119.13]] 11:10, 28 November 2024 (UTC)

What are the odds of rolling 16 or higher on 3D6+D4? 3D6 average 10.5, D4 average is 2.5, total average should be 13. I do not know how to proceed from here. {{unsigned ip|172.71.147.206|01:14, 23 November 2024}}
:By raw combinatorics: 71 + 52 + 34 + 20 + 10 + 4 + 1 ways to get each of 16 - 22 respectively, for a total of 192, out of 4(6^3) = 864 total. 192/864 simplifies to exactly 2/9. I have no idea how Randall found this; if anyone has an idea, please let me know. [[User:Kaisheng21|Kaisheng21]] ([[User talk:Kaisheng21|talk]]) 01:33, 23 November 2024 (UTC)
::I used some simple python code to loop over every dice and confirm and it's 2/9 [[Special:Contributions/162.158.158.111|162.158.158.111]] 12:11, 23 November 2024 (UTC)
::I suspect there is no better way of doing it than looping over the dice. As to how Randall discovered it, it was obvious that at least 2d6 would be needed (since d6 is the only D&D dice that has a multiple of 3 sides), and after that my guess is Randall used a combination of a python script and some experimentation to land on the correct choice of dice. [[Special:Contributions/172.70.162.56|172.70.162.56]] 14:15, 1 December 2024 (UTC)

It seems like we edited the transcript at the same time. The odds of rolling 16 or higher in this situation seem to be 2/9? [[User:Darkmatterisntsquirrels|Darkmatterisntsquirrels]] ([[User talk:Darkmatterisntsquirrels|talk]]) 01:29, 23 November 2024 (UTC)

: There are 864 possible rolls (6 * 6 * 6 * 4). If you enumerate all of the rolls you will find that 192 are 16 or higher. 192/864 = 2/9, the value from the explanation. [[Special:Contributions/172.68.54.139|172.68.54.139]] 01:41, 23 November 2024 (UTC)

I added a table of outcomes to clarify how it works out to 2/9, anyone know how to make it pretty? -- Laurence Cheers {{unsigned ip|172.71.150.247|02:03, 24 November 2024}}

A much simpler approach: Roll two six sided dice and sum the result. You are successful if the result is 5 or 9. That happens 8 times out of 36. 8/36 = 2/9. (Or successful if the sum is 4 or 6, or 2 or 7, or 2,3,4 or 11, or several other combinations.) [[Special:Contributions/172.68.54.139|172.68.54.139]] 01:41, 23 November 2024 (UTC)
:Clever, but dice rolls in D&D involving summing all the dice, applying modifiers, if any, and then comparing to one or more threshold values. Your method makes it very difficult to apply modifiers. [[Special:Contributions/162.158.41.8|162.158.41.8]] 02:49, 23 November 2024 (UTC)
::I think you misunderstand the problem here. This is not skill, no modifiers apply, it's purely probability [[Special:Contributions/162.158.158.111|162.158.158.111]] 12:11, 23 November 2024 (UTC)

Minor quibble, arrows aren't fired (unless they're flaming or self-propelled, perhaps), they are shot. (Shotguns are fired of course.) [[Special:Contributions/162.158.41.73|162.158.41.73]] 02:52, 23 November 2024 (UTC)
:Arrows are "loosed", even more accurately. At least to avoid the confusion from how so many things may be shot, or ''a'' shot. (Many different nouns, from a physical measure of liquer/coffee/vaccine to a projectile, or an even abstract fundemental of chance; and, as verb, projectiles perhps may be shot, then so may their targets.) [[Special:Contributions/172.68.205.178|172.68.205.178]] 14:32, 23 November 2024 (UTC)
:Well, lets not quarrel over it.[[Special:Contributions/172.71.103.67|172.71.103.67]] 14:37, 25 November 2024 (UTC)
:Too many barbed comments, and I'd be all of a quiver... [[Special:Contributions/141.101.99.153|141.101.99.153]] 14:51, 25 November 2024 (UTC)

Rolling 22 or lower on percentile dice (or, equivalently, 79 or higher) is close enough, and easier to come up with. (Give or take whether 00 is treated as 100 or zero.) Or directly represent the action: roll a d10. If it's 1-5, you lose. If it's 6-10, roll again; if it's 1-5 you lose, 6-9 you win, 10 roll again. (Modify slightly if you want to distinguish the case of grabbing *two* cursed arrows.) [[User:Jordan Brown|Jordan Brown]] ([[User talk:Jordan Brown|talk]]) 03:26, 23 November 2024 (UTC)

Alternative exact solution for getting this probability using dice: Roll: 1d8, 2d6, 1d4 succeed on 19 or higher.{{unsigned ip|172.68.55.11|03:54, 23 November 2024}}

I couldn’t remember the formula for binomial coefficients (“n choose k”), but there’s an easy way to calculate that the probability of drawing no cursed arrows is 2/9 without that formula. You just need to multiply the probabilities that each of the arrows drawn is not cursed. Since only two arrows are drawn, you only have to multiply two numbers.

The probability that the first arrow is not cursed is 5/10 – there are 5 non-cursed arrows and 5 cursed arrows out of 10 total. After taking out one non-cursed arrow, there are 4 non-cursed arrows and 5 cursed arrows out of 9 total, so the probability that the second arrow is not cursed is 4/9. Multiplying the two probabilities, the probability of drawing two non-cursed arrows is (4*5)/(10*9) = 20/90 = 2/9.

I was considering writing this observation in the Explanation section of the page, but I’m not if it belongs there. This solution avoids using formulas from combinatorics, so it might not be connected enough to the comic.—[[User:Roryokane|Roryokane]] ([[User talk:Roryokane|talk]]) 06:02, 23 November 2024 (UTC)

My simple-minded approach:
* Roll d10 once for your first arrow: if 1 to 5, the arrow is cursed, otherwise not;
* Roll d10 again for your second arrow: same rules, but repeat until you have a different number from the first one (so d10 is in fact only a d9 this time)
* I won't calculate probabilities – these are your arrows, live with it ;-) [[Special:Contributions/172.69.109.51|172.69.109.51]] 07:33, 23 November 2024 (UTC)
:That has the benefit (over 3d6+1d4) of telling you which arrow(s) (if either) was cursed. [[User:RegularSizedGuy|RegularSizedGuy]] ([[User talk:RegularSizedGuy|talk]]) 07:52, 23 November 2024 (UTC)
::Also tells you how many cursed arrows are left, which is useful if the next player wants to take their chances with them too.[[Special:Contributions/172.71.103.68|172.71.103.68]] 14:40, 25 November 2024 (UTC)
:If you don't like re-rolls, you can make d9 out of 2d3. Nine possibilities, so just assign one of them (perhaps by rolling them one at a time) to be the more significant digit. Don't have a d3 handy? Use d6 and modulo off the extra! (1=1, 2=2, 3=3, 4=1, 5=2, 6=3) [[Special:Contributions/172.68.150.91|172.68.150.91]] 05:59, 24 November 2024 (UTC)

There seems to be doubt that a "N locks and M keys to unlock them" system could be easily accomplished. I think it could be trivial, with strategically interlocking locked-restraints. A chain formed of bike-locks can give a larger locked loop that can be unlocked by just unlocking any ''single'' one of the constituent locks, leaving the other locked loops to not matter (or you could also try the {{w|Borromean rings}} system, whereby it is again secure against itself, until just one ring is opened up to reveal that the rest now ''aren't even locked at all''...). With almost arbitrary ability to cross-link (or, if you will, repeated/alternating-reflected Borromean triplet connections), you can extend the requirements to more than one unlocking being required (by looping chain elements to mre than just the 'adjacent' loops, sideways onto a parallel meta-loop or up/down the chain, all you might do is allow some slack (could be sufficient to get a thing held directly closed by the taut loop-of-loops, but not enough if the passage of the loop through a hasp/sneck actually prevents the otherwise free movement of the final slide-to-unlock action to occur), but a second (or third, or fourth) unlocking can be required to open-end the whole metaloop of locks. At the top end, M=N solutions are also trivial (e.g. two keys, two locks popularly of safety deposit boxes or [[2677: Two Key System|other things]]). Which is not to say that a specific M-of-N puzzle (where 1<M<N) might not need a ''little'' bit of thought to actually design and implement, but there's no obvious reason why all such combinations shouldn't be nicely doable. [[Special:Contributions/172.69.79.165|172.69.79.165]] 14:56, 23 November 2024 (UTC)
:Can we first confirm that the M-of-N Encryption was what Randall was referencing in the first place? [[Special:Contributions/172.71.154.140|172.71.154.140]] 03:17, 24 November 2024 (UTC)
::No, first confirm that this is what the explanation treats as what Randall was referencing. As it was, "complicated lock mechanics" and/or "magic" were suggested as the only ways of doing this, when this (or what we thought this was) just needs a little thought and N bike-locks suitably entangled. [[Special:Contributions/172.70.58.45|172.70.58.45]] 13:17, 24 November 2024 (UTC)
:I'm glad someone else chimed in on this, because it is definitely ''not'' difficult to require unlocking of multiple discrete locks! I can't even figure out why one might think it would be? [[User:ProphetZarquon|ProphetZarquon]] ([[User talk:ProphetZarquon|talk]]) 15:55, 24 November 2024 (UTC)
::I had assumed that the locks were built into the chests (as they sometimes are), and that the chests were physically separated. Using m of n keys on a single chest would merely be complicated, but wouldn't really fulfill the description. Leaving the chests unlocked, but tightly wrapped in a locked chain would be more like drawers of a single "chest". I instead assumed that each of m chests had to be individually opened with its own proper key, but you had n chests to choose from. It was unspecified what would happen if you tried pairing a chest to the wrong key; perhaps both the key and the chest would be disabled (melted/stuck/burned/teleported). (And yes, needing only a subset of the chests, but any sufficiently large subset will do, is a semi-standard class of problem; a search for Byzantine Generals or PAXOS algorithm will get you started.) [[User:JimJJewett|JimJJewett]] ([[User talk:JimJJewett|talk]]) 07:45, 5 December 2024 (UTC)

"other polyhedral dice, with the number of faces denoted by dX (e.g., d10 is a 10-sided die, with numbers from 1 to 10 on it)." - the d10 may be a poor choice as exemplar here; Back in the last century, when I was playing D&D, d10 were typically (and uniquely) numbered 0-9, not 1-10. This may no longer be the case, and I may be showing my age, but if it is still the norm, the d8 or d20 might be a better choice of example. [[Special:Contributions/172.68.210.6|172.68.210.6]] 02:40, 24 November 2024 (UTC)
:Typically, I've only seen 0-9 d10s, as part of a "d100" dice pair, with one reading 0-9 & the other reading 0⁰-9⁰... Single d10, mostly seem to come in 1-10? Maybe it depends which reseller one shops at... [[User:ProphetZarquon|ProphetZarquon]] ([[User talk:ProphetZarquon|talk]]) 15:49, 24 November 2024 (UTC)
::They are usually numbered 0-9, but the 0 represents 10, since writing 10 would require that face to have a different font size. It is still a d10, since the die has ten sides, and still cannot roll at 0. The d100 variant does the same thing with 100, but for the added reason that the 00 face actually does mean 0 when the other die rolls a 1-9. This is the convention, so a die that actually writes 10 on it instead of 0 will be rare. [[User:Stardragon|Stardragon]] ([[User talk:Stardragon|talk]]) 23:14, 24 November 2024 (UTC)

You've all been nerd-sniped. [[User:CalibansCreations|'''Caliban''']] ([[User talk:CalibansCreations|talk]]) 10:53, 24 November 2024 (UTC)

Combinatorics degree? Does such a degree really exist? --[[Special:Contributions/162.158.130.37|162.158.130.37]] 17:19, 24 November 2024 (UTC)
:There are degrees for all kinds of things. A quick search reveals a number of "Combinatorics" or "Combinatorics and <Foo>" (e.g. "Optimisation") degrees. Some of them are marked as Masters degrees, and I haven't dug into the others to see if there are any 'pure' undergraduate ones (apart from anything else, I know there are crucial differences between the structures and scopes of UK and US 'degree courses' to consider, in particular), but there seems to be representation on both sides of the Atlantic (and elsewhere, e.g. Oceana).
:At the very least, it could be a selected specialised segment of an even wider mathematical degree course, or a cross-disciplinary one (like my own, which was part under Physics and part under Computing, but could have included a Stats-based element). [[Special:Contributions/162.158.74.49|162.158.74.49]] 19:07, 24 November 2024 (UTC)
::So "Combinatorics and <Foo>" would be meta-combinatorics, since it is combining something with something else. :) [[User:RandalSchwartz|RandalSchwartz]] ([[User talk:RandalSchwartz|talk]]) 20:19, 28 November 2024 (UTC)
:::I shall do my degree in "Combinatorics, Selectivity, Comparison, Decision Making and/or Cross-Designation (Choose Any Three)"... [[Special:Contributions/172.70.90.5|172.70.90.5]] 21:28, 28 November 2024 (UTC)

I'm trying this on my DM. -[[User:Psychoticpotato|P?sych??otic?pot??at???o ]] ([[User talk:Psychoticpotato|talk]]) 15:11, 25 November 2024 (UTC)

Can someone put into the Explanation the current details regarding the nature of cursed arrows, in whatever edition of DnD we're currently up to. (8th? I've lost track.) In different DnD-like media, I know that it can act somewhat negatively (reduces aim accuracy) or even outright problematic (it curses the person loosing the projectile; or even renders the bow otherwise useless, as analogue to a cursed weapon), or else reduces/inverts the damage (breaks easier, or essentially acts like a thrown beneficial potion to increase health/strength/stamina/etc of the target). I assume that it one of these, from the assumption that the player desires a "good enough" roll to avoid. On the other hand, cursed projectiles could be treated akin to poisoned arrows or vengeful weapons in doing more, better or more targeted damage (in which case it's a powerful aid, the archer is instead taking a chance of using up a stock of 'special arrows', perhaps in line with not knowing whether their foe ''needs'' that extra degree of offensive power). But, at least from the explaining text's approach to dice-roll results, that doesn't exactly mesh with the typical "higher is better" rolling mantra. [[Special:Contributions/172.70.86.129|172.70.86.129]] 22:43, 25 November 2024 (UTC)

I don't think making an M-of-N mechanism with physical locks would be "extremely cumbersome". For example you could have a bolt that must be drawn back to open the mechanism, with several padlocks over it, where the shackle of each padlock blocks the motion of the bolt, such that the distance you can draw the bolt is proportional to how many padlocks are removed. Removing any m of the n padlocks gives you enough range of motion to open the mechanism.
[[Special:Contributions/172.71.154.224|172.71.154.224]] 23:17, 27 November 2024 (UTC)

A DM with a degree in Combinatorics would be unlikely to find this annoying.[[Special:Contributions/162.158.62.245|162.158.62.245]] 05:30, 30 November 2024 (UTC)

With up to three D&D dice, it is impossible to achieve 2/9 exactly. The closest you can get is with d6 + 2d10x10 >= 146 (where d10x10 denotes the tens die, ranging from 10 to 100) yielding a probability of 133/600 = 0.2216667. [[User:Vandof|Vandof]] ([[User talk:Vandof|talk]]) 06:27, 30 November 2024 (UTC)

With four D&D dice, 2d6 + d8 + d10 >= 21 and d10 + 2d12 + d20 >= 36 are alternate solutions. The former is more feasible than 3d6 + d4 for those who don't have three d6's. [[User:Vandof|Vandof]] ([[User talk:Vandof|talk]]) 06:49, 30 November 2024 (UTC)

You can do it with two dice, although not by summation. Roll 2d3; if 1,1, or 3,3 pass, else fail. [[Special:Contributions/162.158.167.88|162.158.167.88]] 19:41, 3 December 2024 (UTC)

Could someone explain option 6, multiplying two six-sided dice, with a threshold of > 20? I think 66, 65, 64, 56, 55, and 46 all work, making it ... equivalent to 1D6.
[[User:JimJJewett|JimJJewett]] ([[User talk:JimJJewett|talk]]) 07:25, 5 December 2024 (UTC)
:It's >= 20, so 54 and 45 work as well. That brings the probability up to 8/36 = 2/9. [[User:Vandof|Vandof]] ([[User talk:Vandof|talk]]) 13:31, 5 December 2024 (UTC)

469: Improvised

2024-12-02T20:53:18Z

Vandof: Fixed: "ao" -> "ago"

{{comic
| number = 469
| date = August 29, 2008
| title = Improvised
| image = improvised.png
| titletext = Oh, your brother is Luke. Sorry, should've mentioned that first.
}}

==Explanation==
In the second of the original ''{{w|Star Wars}}'' film ''{{w|The Empire Strikes Back|Star Wars Episode V: The Empire Strikes Back}}'' (abreviated "ESB" in the comic), just before {{w|Han Solo}}, portrayed by {{w|Harrison Ford}}, is frozen in carbonite, the following conversation occurs:
:Leia: I love you.
:Han: I know.

The original script had Han Solo respond to {{w|Leia}} with "I love you, too," but Harrison Ford felt that the character would not give such a cliched response, even in the face of likely death. He and the director {{w|Irvin Kershner}} changed the line to "I know" before filming. They did, however, also film the scripted version, but it was the "I know" version that was actually used in the finished film.

This line is generally thought to be better than the original would have been. It was long thought that Harrison Ford ad-libbed the line. Others have even suggested it was because they had filmed the scene so many times, that Ford in exasperation at some point just blurted out the "I know" after hearing "I love you" so many times. But it has later been revealed that it was not ad-lib on the spot, although Harrison did suggest the I know line to the director. This has been described here: [https://uk.news.yahoo.com/the-empire-strikes-back-i-love-you-i-know-119550611107.html How the Famous 'I Love You/I Know' Scene From 'The Empire Strikes Back' Really Came Together].

The comic presents several alternative ad-libs that Ford could have made in that conversation, as well as at various points throughout the original trilogy. So in this situation, it is the actor Ford and not Han Solo who speaks the lines.

{| class="wikitable"
! Row
! Col
! Ad-Lib
! Further Detail
|-
| 1
| 1
| '''Well, duh.'''
| Here, Han ruins the mood [a dramatic confession] with a flippant statement.
|-
| 1
| 2
| '''Seriously? ...Christ.'''
| Another example of an out-of-tone ad-lib. The original line is "never tell me the odds," a nod to Solo's daredevil persona. In this ad-lib, however, he is hesitant to try anything dangerous. Additionally, Ford's use of "Christ" would be unfitting, as ''Star Wars'' takes place a long time ago, in a galaxy far, far away, where Christianity is completely unknown. (Still, considering that Solo [[890:_Etymology|named his ship after an Earth bird of prey...]])
|-
| 1
| 3
| '''Oh! Hey, that explains the kissing earlier.'''
| Another absurd, out-of-character answer to a serious remark, this time with Solo acting romantically oblivious [rather than forward, as he is usually].
|-
| 2
| 1
| '''I'm nailing your brother.'''
| So far, Leia doesn't know she has a brother (Luke). Also, since ''to nail'' means to penetrate, she may be surprised to learn that Han is currently engaged in a same-sex relationship (or at least an ongoing arrangement). This panel is referenced in the title text.
|-
| 2
| 2
| '''Hokey religions and ancient weapons are no match for scissors, though they do beat paper and rock.'''
| The original line is "Hokey religions and ancient weapons are no match for a good blaster at your side, kid," a reference to Luke's {{w|The Force|Force}} training and {{w|lightsaber}} use. In this ad-lib, Han turns a discussion about weapons into a [unusually formal] discussion about the game {{w|Rock-paper-scissors}}.
|-
| 2
| 3
| '''Cool. Listen, this thing is really, REALLY cold.'''
| Han is in a freezing chamber in this scene, which are often rather cold.{{Citation needed}} This remark indicates that he is not very interested in Leia's feeling at this moment since he is so cold.
|-
| 3
| 1
| '''Wowzers.'''
| ''Wowzers'' is an expression used by {{w|Inspector Gadget}}; another amusingly out-of-character ad-lib.
|-
| 3
| 2
| '''Barely. They're pretty drunk.'''
| The original response (from the sequel, ''{{w|Star Wars: Episode VI – Return of the Jedi}}'') here is "Uh, my team's ready. I don't have a command crew for the shuttle." In this ad-lib, Han responds to a serious situation [preparations for an important mission to bring down the Galactic Empire] with an un-serious response and an admission that he's allowing his crew to drink while on duty.
|-
| 3
| 3
| '''Man, me too but Chewie never seems interested. Maybe I should grow my hair out.'''
| The original response was "I can arrange that! You could ''use'' a good kiss!" In the original film, Leia's remark "I'd just as soon kiss a {{w|wookiee}}" is meant as an insult to Han, implying that he's no more attractive than a great hairy monster. In this ad-lib, though, Han takes her statement literally, and suggests that he is also interested in kissing a wookiee. Chewbacca is Han's wookiee copilot and fellow smuggler. Han's suggestion that he's interested in kissing Chewbacca is unexpected on many levels: firstly, Han's shown interest in Leia, secondly, Chewbacca is an entirely different species, and thirdly, Chewbacca is also male, and Han Solo is presumed by Leia to be straight.
|}

Note: although it's spelled "wookie" in the comic, the canonical spelling of Chewbacca's species is "{{w|Wookiee}}".

The title text continues the ad-lib in panel four. It refers to the plot twist that {{w|Luke Skywalker}} is Princess {{w|Princess Leia|Leia's}} brother, which would not be revealed until the next film in the series. How Harrison Ford knows this twist at this point in the story is unknown.

==Transcript==
:[Caption above the panels:]
:Harrison Ford famously improvised his "I know" line in E.S.B. Here are a few of his less-successful ad-libs:

:[Harrison Ford as Han Solo (in all the panels) stands in front of Princess Leia on the Cloud City Carbon Freezing Chamber.]
:Leia: I love you.
:Han: Well, duh.

:[Han Solo in the cockpit of the Millennium Falcon.]
:C-3P0: Sir, the possibility of successfully navigating an asteroid field is approximately 3720 to 1!
:Han: Seriously? ...Christ.

:[Han Solo stands in front of Princess Leia on the Cloud City Carbon Freezing Chamber.]
:Leia: I love you.
:Han: Oh! Hey, that explains the kissing earlier.

:[Han Solo stands in front of Princess Leia on the Cloud City Carbon Freezing Chamber.]
:Leia: I love you.
:Han: I'm nailing your brother.

:[Han Solo standing in front of Luke Skywalker, who is holding a blast shield helmet and a lightsaber. The training droid hovers between them.]

:Han: Hokey religions and ancient weapons are no match for scissors, though they do beat paper and rock.

:[Han Solo stands in front of Princess Leia on the Cloud City Carbon Freezing Chamber.]
:Leia: I love you.
:Han: Cool. Listen, this thing is really, really cold.

:[Han Solo stands in front of Princess Leia on the Cloud City Carbon Freezing Chamber.]
:Leia: I love you.
:Han: Wowzers.

:[Han Solo sits with two others. General Madine approaches.]
:Madine: General Solo, is your strike team assembled?
:Han: Barely. They're pretty drunk.

:[Han Solo and Princess Leia stand in an Ice Tunnel of Hoth.]
:Leia: I'd just as soon kiss a wookie.
:Han: Man, me too but Chewie never seems interested. Maybe I should grow my hair out.

{{comic discussion}}
[[Category:Comics featuring real people]]
[[Category:Comics featuring Cueball]]
[[Category:Multiple Cueballs]]
[[Category:Star Wars]]
[[Category:Sex]]
[[Category:Romance]]
[[Category:Homosexuality]]

3015: D&D Combinatorics

2024-12-02T17:30:40Z

Vandof: Added alternative method

{{comic
| number = 3015
| date = November 22, 2024
| title = D&D Combinatorics
| image = dnd_combinatorics_2x.png
| imagesize = 328x446px
| noexpand = true
| titletext = Look, you can't complain about this after giving us so many scenarios involving N locked chests and M unlabeled keys.
}}

==Explanation==
{{incomplete|Created by a HTML SHORTENING CODE TYPO - Please change this comment when editing this page. Please DO delete this tag too soon.}}

{{w|Dungeons and Dragons}} (D&D) is a {{w|tabletop role-playing game}} that usually has a "Dungeon Master" (narrator) that takes a team of players through scenarios where they attack monsters and go on quests.

Often, there will be semi-random events: e.g., when attacking a monster, often a player will roll a die and deal damage based on the result. D&D uses a variety of dice, from regular d6 (6-sided, cubic dice) to other {{w|Dice#Common_variations|polyhedral dice}}, with the number of faces denoted by XdY (e.g., 3d10 is a rolling of 3 10-sided die, which each have numbers from 1 to 10 on it). Common sets include: d4, d6, d8, d10, d12, d20, and occasionally d100 (typically not, however, the [[2626:_d65536|d65536]]).{{cn}}

With these, you can simulate events with a wide variety of denominators. In this case, Cueball gives a {{w|combinatorics|combinatorial}} problem:

* There are 10 arrows.
* 5 arrows are cursed.
* You randomly take two.
* What are the odds that neither of them are cursed?

Calculating using {{w|binomial coefficients}}, there are "10 choose 2" (45) ways to choose two arrows, of which there are "5 choose 2" (10) ways to choose 2 arrows that are non-cursed. As a result, the odds of taking all non-cursed arrows is 10/45, which simplifies to 2/9.

To see this in a different way, the probability of choosing one non-cursed arrow is 5/10, which then must be multiplied by the probability of choosing the second non-cursed arrow, which is now 4/9, giving 20/90 or 2/9, the same result as before.

The Dungeon Master (DM) in this case [[356: Nerd Sniping|has to]] map that probability into rolling multiple dice, whose sums are also not evenly distributed: i.e. if rolling 3d6 (3 six-sided dice) and a d4 (1 four-sided die), the sums can range from 4 to 22. It's pretty hard to do this in one's head, but it does happen that the odds of rolling 16 or more with this combination is 2/9, matching the probability that we want to simulate. Here's a table of all the 6*6*6*4=864 possible outcomes -

{| class="wikitable"
|+ All possible combinations of rolls for 3d6 + 1d4
|-
!Total!!4!!5!!6!!7!!8!!9!!10!!11!!12!!13!!14!!15!!16!!17!!18!!19!!20!!21!!22
|-
|Ways to roll it||1||4||10||20||34||52||71||88||100||104||100||88
| style="background:#ffffcc;" | ''' ''71'' '''
| style="background:#ffffcc;" | ''' ''52'' '''
| style="background:#ffffcc;" | ''' ''34'' '''
| style="background:#ffffcc;" | ''' ''20'' '''
| style="background:#ffffcc;" | ''' ''10'' '''
| style="background:#ffffcc;" | ''' ''4'' '''
| style="background:#ffffcc;" | ''' ''1'' '''
|}

71+52+34+20+10+4+1 = 192

192/864 = 2/9, which matches the desired probability from earlier. The table of outcomes can either be bruteforced with a program, or can be derived using generating functions.

The caption elaborates that the DM has a degree in the relevant field, and is unable to resist applying this to the D&D game when the opportunity arises - opportunities that Cueball eagerly provides for this very reason.

There are several much easier ways of implementing this operation, without coming up with a more complex solution:
#Do not even attempt to abstract the chances with dice-rolls. Literally present 10 similar-looking arrows, or other objects that are taken to represent arrows (face-down playing cards, for example), where the assigned information of whether each one is cursed initially hidden away from Cueball, and then just let Cueball pick any two. This approach would more likely be used if the D&D gameplay were {{w|Live action role-playing game|live-action}} as opposed to {{w|Tabletop role-playing game|tabletop}} (though is still possible in tabletop).
#Even just with D&D dice, the DM could ask Cueball to roll a 1d10 for the first arrow, and then again for the second, re-rolling the second so long as Cueball gets the same number as before (which emulates the same sort of process, but with a non-zero chance of having to make and reject an arbitrary number of extra dice-rolls). One could specify that 1-5 represents the cursed arrows and 6-10 represents the non-cursed arrows, following the convention that lower rolls are bad in D&D.
#Similarly, the player could be asked to roll a d20, with a score of 15 or 16 requiring a re-roll and 17–20 being successful choices. This would give a 4/18 chance, i.e., 2/9 for a successful roll on the first (and any subsequent) rolls. As with option 2, there would be a 1/10 chance of having to make and reject at least one extra dice-roll.
#If understanding the actual odds, but wishing to keep the dice in use simple, a 2/9 probability can also be found by saying Cueball would succeed when 2D6 produces a 9, 10, or 12 (4/36, 3/36, and 1/36 probability, respectively, giving 8/36, i.e., 2/9).
#Another method would be to roll 1d6 twice, using the first as a base number and the second as a control die where 1-2 = +0, 3-4 = +6 and 5-6 = +12 for a linear spread of 1-18. In this case a roll of 3, 4, 5, or 6 on the first roll coupled with a 5 or 6 on the second roll would indicate the top four of the eighteen possibilities, 4/18, or 2/9.
#Or to roll 1d6 twice and ''multiply'', rather than add, the results. A successful roll is 20 or more.
#Or to take the maximum of 1d6 and 1d12. Denoting 4 or lower as a successful roll, the method yields a probability of 16/72 = 2/9.
#Alternatively, approximate the odds by using a d100 (or equivalent roll of two D10s) and seeking an 78 or higher (i.e. the range of 78-99, assuming this roll can produce a zero/double-zero roll, instead of a 'natural 100' for which the range would have to start at 79), which gives a 22% chance, which may be sufficiently acceptable as it is substantially similar to 2/9's effective odds of 22.222%. If you re-roll either the 0 or 100 (depending on whether you use 78 or 79 as the cutoff), you would bring the probability exactly to 22/99 or 2/9.

The first two options also instantly reveal cases of whether ''two'' cursed arrows are nominally chosen (an outcome that is at identical odds to the opposite possibility of neither being so), should this be useful roleplaying information in addition to the basic fact of ''failing'' to avoid at least one of them. The fourth option could also be used to suggest this if (for example) the complementary results of 2, 4 or 5 are rolled, and the final one in the event that the 'percentage' given is 0-21 (or 1-22).

One could argue that the above solutions do not have the "polished" D&D feel of rolling a certain number of dice, adding them up, and seeing if the result is greater than or equal to an entirely correct required total. This is a commonly used mechanic for difficulty checks, hit calculations, and other such chance-based events in D&D. The DM may feel that this dice format is a requirement, but this approach is far too clunky for most DMs to be practical. It may be inferred that as the DM's mind tends towards more combinatorial solutions, she is either unable or unwilling to consider more straightforward and less time-consuming solutions to this cursed arrow problem.

The title text claims that Randall only started doing this to the DM after she herself insisted on forcing another combinatorial puzzle on the players several times, involving a bunch of locked treasure chests and a multitude of keys to unlock them with. This might be a reference to an M-of-N encryption system, where a system has ''n'' valid passwords (instead of just one) but requires ''m'' of those passwords to be given before it will open; it is assumed m is greater than 1 but less than n. While this is easy enough to implement in a computer system, it would be extremely cumbersome to build for a physical lock with keys, and spreading the mechanism across multiple separate treasure chests would be impossible without literal magic (luckily, magic is in plentiful supply in a typical Dungeons and Dragons game).{{cn}}

==Transcript==
:[Cueball, Megan, Ponytail, White Hat, and Knit Cap are sitting around a table on office chairs. The first and last at either end and the other on the same side facing outwards. Everyone is looking at Cueball who is holding a finger up in front of him while speaking. Ponytail is facepalming while replying. The table is covered in sheets of paper and assorted dice.]
:Cueball: I grab 2 of the 10 arrows without looking and fire them, hoping I didn't grab one of the 5 cursed ones. Did I?
:Ponytail: Sigh. Umm. Okay.
:Ponytail: Roll... Uh... Hang on...
:Ponytail: Roll 3d6 and a d4. You need... 16 or better to avoid the cursed arrows.

:[Caption below the panel:]
:I got '''''way''''' more annoying to play D&D with once I learned that our DM has a combinatorics degree and can't resist puzzles.

==Trivia==
When this comic was originally released, due to seeming error on Randall's end, the official title of the page was "xkcd: D[sic] Combinatorics", instead of "xkcd: D&D Combinatorics". The reason for this is thought to be caused by literal interpretation of the '''''&D''''' as an HTML escape character.
{{comic discussion}}

[[Category:Comics featuring Cueball]]
[[Category:Comics featuring Megan]]
[[Category:Comics featuring Ponytail]]
[[Category:Comics featuring White Hat]]
[[Category:Comics featuring Knit Cap]]
[[Category:Games]]
[[Category:Math]]

Talk:3015: D&D Combinatorics

2024-11-30T06:49:05Z

Vandof: Added and edited comment

The bot originally created this page as “D Combinatorics”. I renamed it to the correct title and tried to get as many of the references as possible (including a few redirects). [[User:JBYoshi|JBYoshi]] ([[User talk:JBYoshi|talk]]) 00:54, 23 November 2024 (UTC)

:The title in the Atom feed (which I'm assuming the bot consumes) is "D Combinatorics". I'm guessing something in Randall's pipeline didn't like the ampersand. --[[Special:Contributions/162.158.154.160|162.158.154.160]] 01:41, 23 November 2024 (UTC)

::Yup, if you look at [https://xkcd.com/3015/info.0.json 3015's JSON] you see that <code>title</code> and <code>safe_title</code> differ, and if you look at the HTML page source you'll see '''3''' different things: <code><title>xkcd: D Combinatorics</title></code>, <code><meta property="og:title" content="D&amp;D Combinatorics"></code>, and <code><div id="ctitle">D&D Combinatorics</div></code>! So probably what happened is Randall entered D&D but was supposed to enter D&amp;D, and the openGraph tags adder code, having to be HTML-aware, decoded & normalized D&D as HTML would, but the other parts of the pipeline just ate it for some reason. {{unsigned ip|172.69.65.224|06:09, 23 November 2024}}

::: The problem now is that the feed doesn't validate (because it contains a bare &) and it's also not updating (maybe because of the previous problem). --[[Special:Contributions/172.71.119.13|172.71.119.13]] 11:10, 28 November 2024 (UTC)

What are the odds of rolling 16 or higher on 3D6+D4? 3D6 average 10.5, D4 average is 2.5, total average should be 13. I do not know how to proceed from here. {{unsigned ip|172.71.147.206|01:14, 23 November 2024}}
:By raw combinatorics: 71 + 52 + 34 + 20 + 10 + 4 + 1 ways to get each of 16 - 22 respectively, for a total of 192, out of 4(6^3) = 864 total. 192/864 simplifies to exactly 2/9. I have no idea how Randall found this; if anyone has an idea, please let me know. [[User:Kaisheng21|Kaisheng21]] ([[User talk:Kaisheng21|talk]]) 01:33, 23 November 2024 (UTC)
::I used some simple python code to loop over every dice and confirm and it's 2/9 [[Special:Contributions/162.158.158.111|162.158.158.111]] 12:11, 23 November 2024 (UTC)

It seems like we edited the transcript at the same time. The odds of rolling 16 or higher in this situation seem to be 2/9? [[User:Darkmatterisntsquirrels|Darkmatterisntsquirrels]] ([[User talk:Darkmatterisntsquirrels|talk]]) 01:29, 23 November 2024 (UTC)

: There are 864 possible rolls (6 * 6 * 6 * 4). If you enumerate all of the rolls you will find that 192 are 16 or higher. 192/864 = 2/9, the value from the explanation. [[Special:Contributions/172.68.54.139|172.68.54.139]] 01:41, 23 November 2024 (UTC)

I added a table of outcomes to clarify how it works out to 2/9, anyone know how to make it pretty? -- Laurence Cheers {{unsigned ip|172.71.150.247|02:03, 24 November 2024}}

A much simpler approach: Roll two six sided dice and sum the result. You are successful if the result is 5 or 9. That happens 8 times out of 36. 8/36 = 2/9. (Or successful if the sum is 4 or 6, or 2 or 7, or 2,3,4 or 11, or several other combinations.) [[Special:Contributions/172.68.54.139|172.68.54.139]] 01:41, 23 November 2024 (UTC)
:Clever, but dice rolls in D&D involving summing all the dice, applying modifiers, if any, and then comparing to one or more threshold values. Your method makes it very difficult to apply modifiers. [[Special:Contributions/162.158.41.8|162.158.41.8]] 02:49, 23 November 2024 (UTC)
::I think you misunderstand the problem here. This is not skill, no modifiers apply, it's purely probability [[Special:Contributions/162.158.158.111|162.158.158.111]] 12:11, 23 November 2024 (UTC)

Minor quibble, arrows aren't fired (unless they're flaming or self-propelled, perhaps), they are shot. (Shotguns are fired of course.) [[Special:Contributions/162.158.41.73|162.158.41.73]] 02:52, 23 November 2024 (UTC)
:Arrows are "loosed", even more accurately. At least to avoid the confusion from how so many things may be shot, or ''a'' shot. (Many different nouns, from a physical measure of liquer/coffee/vaccine to a projectile, or an even abstract fundemental of chance; and, as verb, projectiles perhps may be shot, then so may their targets.) [[Special:Contributions/172.68.205.178|172.68.205.178]] 14:32, 23 November 2024 (UTC)
:Well, lets not quarrel over it.[[Special:Contributions/172.71.103.67|172.71.103.67]] 14:37, 25 November 2024 (UTC)
:Too many barbed comments, and I'd be all of a quiver... [[Special:Contributions/141.101.99.153|141.101.99.153]] 14:51, 25 November 2024 (UTC)

Rolling 22 or lower on percentile dice (or, equivalently, 79 or higher) is close enough, and easier to come up with. (Give or take whether 00 is treated as 100 or zero.) Or directly represent the action: roll a d10. If it's 1-5, you lose. If it's 6-10, roll again; if it's 1-5 you lose, 6-9 you win, 10 roll again. (Modify slightly if you want to distinguish the case of grabbing *two* cursed arrows.) [[User:Jordan Brown|Jordan Brown]] ([[User talk:Jordan Brown|talk]]) 03:26, 23 November 2024 (UTC)

Alternative exact solution for getting this probability using dice: Roll: 1d8, 2d6, 1d4 succeed on 19 or higher.{{unsigned ip|172.68.55.11|03:54, 23 November 2024}}

I couldn’t remember the formula for binomial coefficients (“n choose k”), but there’s an easy way to calculate that the probability of drawing no cursed arrows is 2/9 without that formula. You just need to multiply the probabilities that each of the arrows drawn is not cursed. Since only two arrows are drawn, you only have to multiply two numbers.

The probability that the first arrow is not cursed is 5/10 – there are 5 non-cursed arrows and 5 cursed arrows out of 10 total. After taking out one non-cursed arrow, there are 4 non-cursed arrows and 5 cursed arrows out of 9 total, so the probability that the second arrow is not cursed is 4/9. Multiplying the two probabilities, the probability of drawing two non-cursed arrows is (4*5)/(10*9) = 20/90 = 2/9.

I was considering writing this observation in the Explanation section of the page, but I’m not if it belongs there. This solution avoids using formulas from combinatorics, so it might not be connected enough to the comic.—[[User:Roryokane|Roryokane]] ([[User talk:Roryokane|talk]]) 06:02, 23 November 2024 (UTC)

My simple-minded approach:
* Roll d10 once for your first arrow: if 1 to 5, the arrow is cursed, otherwise not;
* Roll d10 again for your second arrow: same rules, but repeat until you have a different number from the first one (so d10 is in fact only a d9 this time)
* I won't calculate probabilities – these are your arrows, live with it ;-) [[Special:Contributions/172.69.109.51|172.69.109.51]] 07:33, 23 November 2024 (UTC)
:That has the benefit (over 3d6+1d4) of telling you which arrow(s) (if either) was cursed. [[User:RegularSizedGuy|RegularSizedGuy]] ([[User talk:RegularSizedGuy|talk]]) 07:52, 23 November 2024 (UTC)
::Also tells you how many cursed arrows are left, which is useful if the next player wants to take their chances with them too.[[Special:Contributions/172.71.103.68|172.71.103.68]] 14:40, 25 November 2024 (UTC)
:If you don't like re-rolls, you can make d9 out of 2d3. Nine possibilities, so just assign one of them (perhaps by rolling them one at a time) to be the more significant digit. Don't have a d3 handy? Use d6 and modulo off the extra! (1=1, 2=2, 3=3, 4=1, 5=2, 6=3) [[Special:Contributions/172.68.150.91|172.68.150.91]] 05:59, 24 November 2024 (UTC)

There seems to be doubt that a "N locks and M keys to unlock them" system could be easily accomplished. I think it could be trivial, with strategically interlocking locked-restraints. A chain formed of bike-locks can give a larger locked loop that can be unlocked by just unlocking any ''single'' one of the constituent locks, leaving the other locked loops to not matter (or you could also try the {{w|Borromean rings}} system, whereby it is again secure against itself, until just one ring is opened up to reveal that the rest now ''aren't even locked at all''...). With almost arbitrary ability to cross-link (or, if you will, repeated/alternating-reflected Borromean triplet connections), you can extend the requirements to more than one unlocking being required (by looping chain elements to mre than just the 'adjacent' loops, sideways onto a parallel meta-loop or up/down the chain, all you might do is allow some slack (could be sufficient to get a thing held directly closed by the taut loop-of-loops, but not enough if the passage of the loop through a hasp/sneck actually prevents the otherwise free movement of the final slide-to-unlock action to occur), but a second (or third, or fourth) unlocking can be required to open-end the whole metaloop of locks. At the top end, M=N solutions are also trivial (e.g. two keys, two locks popularly of safety deposit boxes or [[2677: Two Key System|other things]]). Which is not to say that a specific M-of-N puzzle (where 1<M<N) might not need a ''little'' bit of thought to actually design and implement, but there's no obvious reason why all such combinations shouldn't be nicely doable. [[Special:Contributions/172.69.79.165|172.69.79.165]] 14:56, 23 November 2024 (UTC)
:Can we first confirm that the M-of-N Encryption was what Randall was referencing in the first place? [[Special:Contributions/172.71.154.140|172.71.154.140]] 03:17, 24 November 2024 (UTC)
::No, first confirm that this is what the explanation treats as what Randall was referencing. As it was, "complicated lock mechanics" and/or "magic" were suggested as the only ways of doing this, when this (or what we thought this was) just needs a little thought and N bike-locks suitably entangled. [[Special:Contributions/172.70.58.45|172.70.58.45]] 13:17, 24 November 2024 (UTC)
:I'm glad someone else chimed in on this, because it is definitely ''not'' difficult to require unlocking of multiple discrete locks! I can't even figure out why one might think it would be? [[User:ProphetZarquon|ProphetZarquon]] ([[User talk:ProphetZarquon|talk]]) 15:55, 24 November 2024 (UTC)

"other polyhedral dice, with the number of faces denoted by dX (e.g., d10 is a 10-sided die, with numbers from 1 to 10 on it)." - the d10 may be a poor choice as exemplar here; Back in the last century, when I was playing D&D, d10 were typically (and uniquely) numbered 0-9, not 1-10. This may no longer be the case, and I may be showing my age, but if it is still the norm, the d8 or d20 might be a better choice of example. [[Special:Contributions/172.68.210.6|172.68.210.6]] 02:40, 24 November 2024 (UTC)
:Typically, I've only seen 0-9 d10s, as part of a "d100" dice pair, with one reading 0-9 & the other reading 0⁰-9⁰... Single d10, mostly seem to come in 1-10? Maybe it depends which reseller one shops at... [[User:ProphetZarquon|ProphetZarquon]] ([[User talk:ProphetZarquon|talk]]) 15:49, 24 November 2024 (UTC)
::They are usually numbered 0-9, but the 0 represents 10, since writing 10 would require that face to have a different font size. It is still a d10, since the die has ten sides, and still cannot roll at 0. The d100 variant does the same thing with 100, but for the added reason that the 00 face actually does mean 0 when the other die rolls a 1-9. This is the convention, so a die that actually writes 10 on it instead of 0 will be rare. [[User:Stardragon|Stardragon]] ([[User talk:Stardragon|talk]]) 23:14, 24 November 2024 (UTC)

You've all been nerd-sniped. [[User:CalibansCreations|'''Caliban''']] ([[User talk:CalibansCreations|talk]]) 10:53, 24 November 2024 (UTC)

Combinatorics degree? Does such a degree really exist? --[[Special:Contributions/162.158.130.37|162.158.130.37]] 17:19, 24 November 2024 (UTC)
:There are degrees for all kinds of things. A quick search reveals a number of "Combinatorics" or "Combinatorics and <Foo>" (e.g. "Optimisation") degrees. Some of them are marked as Masters degrees, and I haven't dug into the others to see if there are any 'pure' undergraduate ones (apart from anything else, I know there are crucial differences between the structures and scopes of UK and US 'degree courses' to consider, in particular), but there seems to be representation on both sides of the Atlantic (and elsewhere, e.g. Oceana).
:At the very least, it could be a selected specialised segment of an even wider mathematical degree course, or a cross-disciplinary one (like my own, which was part under Physics and part under Computing, but could have included a Stats-based element). [[Special:Contributions/162.158.74.49|162.158.74.49]] 19:07, 24 November 2024 (UTC)
::So "Combinatorics and <Foo>" would be meta-combinatorics, since it is combining something with something else. :) [[User:RandalSchwartz|RandalSchwartz]] ([[User talk:RandalSchwartz|talk]]) 20:19, 28 November 2024 (UTC)
:::I shall do my degree in "Combinatorics, Selectivity, Comparison, Decision Making and/or Cross-Designation (Choose Any Three)"... [[Special:Contributions/172.70.90.5|172.70.90.5]] 21:28, 28 November 2024 (UTC)

I'm trying this on my DM. -[[User:Psychoticpotato|P?sych??otic?pot??at???o ]] ([[User talk:Psychoticpotato|talk]]) 15:11, 25 November 2024 (UTC)

Can someone put into the Explanation the current details regarding the nature of cursed arrows, in whatever edition of DnD we're currently up to. (8th? I've lost track.) In different DnD-like media, I know that it can act somewhat negatively (reduces aim accuracy) or even outright problematic (it curses the person loosing the projectile; or even renders the bow otherwise useless, as analogue to a cursed weapon), or else reduces/inverts the damage (breaks easier, or essentially acts like a thrown beneficial potion to increase health/strength/stamina/etc of the target). I assume that it one of these, from the assumption that the player desires a "good enough" roll to avoid. On the other hand, cursed projectiles could be treated akin to poisoned arrows or vengeful weapons in doing more, better or more targeted damage (in which case it's a powerful aid, the archer is instead taking a chance of using up a stock of 'special arrows', perhaps in line with not knowing whether their foe ''needs'' that extra degree of offensive power). But, at least from the explaining text's approach to dice-roll results, that doesn't exactly mesh with the typical "higher is better" rolling mantra. [[Special:Contributions/172.70.86.129|172.70.86.129]] 22:43, 25 November 2024 (UTC)

I don't think making an M-of-N mechanism with physical locks would be "extremely cumbersome". For example you could have a bolt that must be drawn back to open the mechanism, with several padlocks over it, where the shackle of each padlock blocks the motion of the bolt, such that the distance you can draw the bolt is proportional to how many padlocks are removed. Removing any m of the n padlocks gives you enough range of motion to open the mechanism.
[[Special:Contributions/172.71.154.224|172.71.154.224]] 23:17, 27 November 2024 (UTC)

A DM with a degree in Combinatorics would be unlikely to find this annoying.[[Special:Contributions/162.158.62.245|162.158.62.245]] 05:30, 30 November 2024 (UTC)

With up to three D&D dice, it is impossible to achieve 2/9 exactly. The closest you can get is with d6 + 2d10x10 >= 146 (where d10x10 denotes the tens die, ranging from 10 to 100) yielding a probability of 133/600 = 0.2216667. [[User:Vandof|Vandof]] ([[User talk:Vandof|talk]]) 06:27, 30 November 2024 (UTC)

With four D&D dice, 2d6 + d8 + d10 >= 21 and d10 + 2d12 + d20 >= 36 are alternate solutions. The former is more feasible than 3d6 + d4 for those who don't have three d6's. [[User:Vandof|Vandof]] ([[User talk:Vandof|talk]]) 06:49, 30 November 2024 (UTC)

Talk:3015: D&D Combinatorics

2024-11-30T06:27:11Z

Vandof: Added comment

The bot originally created this page as “D Combinatorics”. I renamed it to the correct title and tried to get as many of the references as possible (including a few redirects). [[User:JBYoshi|JBYoshi]] ([[User talk:JBYoshi|talk]]) 00:54, 23 November 2024 (UTC)

:The title in the Atom feed (which I'm assuming the bot consumes) is "D Combinatorics". I'm guessing something in Randall's pipeline didn't like the ampersand. --[[Special:Contributions/162.158.154.160|162.158.154.160]] 01:41, 23 November 2024 (UTC)

::Yup, if you look at [https://xkcd.com/3015/info.0.json 3015's JSON] you see that <code>title</code> and <code>safe_title</code> differ, and if you look at the HTML page source you'll see '''3''' different things: <code><title>xkcd: D Combinatorics</title></code>, <code><meta property="og:title" content="D&amp;D Combinatorics"></code>, and <code><div id="ctitle">D&D Combinatorics</div></code>! So probably what happened is Randall entered D&D but was supposed to enter D&amp;D, and the openGraph tags adder code, having to be HTML-aware, decoded & normalized D&D as HTML would, but the other parts of the pipeline just ate it for some reason. {{unsigned ip|172.69.65.224|06:09, 23 November 2024}}

::: The problem now is that the feed doesn't validate (because it contains a bare &) and it's also not updating (maybe because of the previous problem). --[[Special:Contributions/172.71.119.13|172.71.119.13]] 11:10, 28 November 2024 (UTC)

What are the odds of rolling 16 or higher on 3D6+D4? 3D6 average 10.5, D4 average is 2.5, total average should be 13. I do not know how to proceed from here. {{unsigned ip|172.71.147.206|01:14, 23 November 2024}}
:By raw combinatorics: 71 + 52 + 34 + 20 + 10 + 4 + 1 ways to get each of 16 - 22 respectively, for a total of 192, out of 4(6^3) = 864 total. 192/864 simplifies to exactly 2/9. I have no idea how Randall found this; if anyone has an idea, please let me know. [[User:Kaisheng21|Kaisheng21]] ([[User talk:Kaisheng21|talk]]) 01:33, 23 November 2024 (UTC)
::I used some simple python code to loop over every dice and confirm and it's 2/9 [[Special:Contributions/162.158.158.111|162.158.158.111]] 12:11, 23 November 2024 (UTC)

It seems like we edited the transcript at the same time. The odds of rolling 16 or higher in this situation seem to be 2/9? [[User:Darkmatterisntsquirrels|Darkmatterisntsquirrels]] ([[User talk:Darkmatterisntsquirrels|talk]]) 01:29, 23 November 2024 (UTC)

: There are 864 possible rolls (6 * 6 * 6 * 4). If you enumerate all of the rolls you will find that 192 are 16 or higher. 192/864 = 2/9, the value from the explanation. [[Special:Contributions/172.68.54.139|172.68.54.139]] 01:41, 23 November 2024 (UTC)

I added a table of outcomes to clarify how it works out to 2/9, anyone know how to make it pretty? -- Laurence Cheers {{unsigned ip|172.71.150.247|02:03, 24 November 2024}}

A much simpler approach: Roll two six sided dice and sum the result. You are successful if the result is 5 or 9. That happens 8 times out of 36. 8/36 = 2/9. (Or successful if the sum is 4 or 6, or 2 or 7, or 2,3,4 or 11, or several other combinations.) [[Special:Contributions/172.68.54.139|172.68.54.139]] 01:41, 23 November 2024 (UTC)
:Clever, but dice rolls in D&D involving summing all the dice, applying modifiers, if any, and then comparing to one or more threshold values. Your method makes it very difficult to apply modifiers. [[Special:Contributions/162.158.41.8|162.158.41.8]] 02:49, 23 November 2024 (UTC)
::I think you misunderstand the problem here. This is not skill, no modifiers apply, it's purely probability [[Special:Contributions/162.158.158.111|162.158.158.111]] 12:11, 23 November 2024 (UTC)

Minor quibble, arrows aren't fired (unless they're flaming or self-propelled, perhaps), they are shot. (Shotguns are fired of course.) [[Special:Contributions/162.158.41.73|162.158.41.73]] 02:52, 23 November 2024 (UTC)
:Arrows are "loosed", even more accurately. At least to avoid the confusion from how so many things may be shot, or ''a'' shot. (Many different nouns, from a physical measure of liquer/coffee/vaccine to a projectile, or an even abstract fundemental of chance; and, as verb, projectiles perhps may be shot, then so may their targets.) [[Special:Contributions/172.68.205.178|172.68.205.178]] 14:32, 23 November 2024 (UTC)
:Well, lets not quarrel over it.[[Special:Contributions/172.71.103.67|172.71.103.67]] 14:37, 25 November 2024 (UTC)
:Too many barbed comments, and I'd be all of a quiver... [[Special:Contributions/141.101.99.153|141.101.99.153]] 14:51, 25 November 2024 (UTC)

Rolling 22 or lower on percentile dice (or, equivalently, 79 or higher) is close enough, and easier to come up with. (Give or take whether 00 is treated as 100 or zero.) Or directly represent the action: roll a d10. If it's 1-5, you lose. If it's 6-10, roll again; if it's 1-5 you lose, 6-9 you win, 10 roll again. (Modify slightly if you want to distinguish the case of grabbing *two* cursed arrows.) [[User:Jordan Brown|Jordan Brown]] ([[User talk:Jordan Brown|talk]]) 03:26, 23 November 2024 (UTC)

Alternative exact solution for getting this probability using dice: Roll: 1d8, 2d6, 1d4 succeed on 19 or higher.{{unsigned ip|172.68.55.11|03:54, 23 November 2024}}

I couldn’t remember the formula for binomial coefficients (“n choose k”), but there’s an easy way to calculate that the probability of drawing no cursed arrows is 2/9 without that formula. You just need to multiply the probabilities that each of the arrows drawn is not cursed. Since only two arrows are drawn, you only have to multiply two numbers.

The probability that the first arrow is not cursed is 5/10 – there are 5 non-cursed arrows and 5 cursed arrows out of 10 total. After taking out one non-cursed arrow, there are 4 non-cursed arrows and 5 cursed arrows out of 9 total, so the probability that the second arrow is not cursed is 4/9. Multiplying the two probabilities, the probability of drawing two non-cursed arrows is (4*5)/(10*9) = 20/90 = 2/9.

I was considering writing this observation in the Explanation section of the page, but I’m not if it belongs there. This solution avoids using formulas from combinatorics, so it might not be connected enough to the comic.—[[User:Roryokane|Roryokane]] ([[User talk:Roryokane|talk]]) 06:02, 23 November 2024 (UTC)

My simple-minded approach:
* Roll d10 once for your first arrow: if 1 to 5, the arrow is cursed, otherwise not;
* Roll d10 again for your second arrow: same rules, but repeat until you have a different number from the first one (so d10 is in fact only a d9 this time)
* I won't calculate probabilities – these are your arrows, live with it ;-) [[Special:Contributions/172.69.109.51|172.69.109.51]] 07:33, 23 November 2024 (UTC)
:That has the benefit (over 3d6+1d4) of telling you which arrow(s) (if either) was cursed. [[User:RegularSizedGuy|RegularSizedGuy]] ([[User talk:RegularSizedGuy|talk]]) 07:52, 23 November 2024 (UTC)
::Also tells you how many cursed arrows are left, which is useful if the next player wants to take their chances with them too.[[Special:Contributions/172.71.103.68|172.71.103.68]] 14:40, 25 November 2024 (UTC)
:If you don't like re-rolls, you can make d9 out of 2d3. Nine possibilities, so just assign one of them (perhaps by rolling them one at a time) to be the more significant digit. Don't have a d3 handy? Use d6 and modulo off the extra! (1=1, 2=2, 3=3, 4=1, 5=2, 6=3) [[Special:Contributions/172.68.150.91|172.68.150.91]] 05:59, 24 November 2024 (UTC)

There seems to be doubt that a "N locks and M keys to unlock them" system could be easily accomplished. I think it could be trivial, with strategically interlocking locked-restraints. A chain formed of bike-locks can give a larger locked loop that can be unlocked by just unlocking any ''single'' one of the constituent locks, leaving the other locked loops to not matter (or you could also try the {{w|Borromean rings}} system, whereby it is again secure against itself, until just one ring is opened up to reveal that the rest now ''aren't even locked at all''...). With almost arbitrary ability to cross-link (or, if you will, repeated/alternating-reflected Borromean triplet connections), you can extend the requirements to more than one unlocking being required (by looping chain elements to mre than just the 'adjacent' loops, sideways onto a parallel meta-loop or up/down the chain, all you might do is allow some slack (could be sufficient to get a thing held directly closed by the taut loop-of-loops, but not enough if the passage of the loop through a hasp/sneck actually prevents the otherwise free movement of the final slide-to-unlock action to occur), but a second (or third, or fourth) unlocking can be required to open-end the whole metaloop of locks. At the top end, M=N solutions are also trivial (e.g. two keys, two locks popularly of safety deposit boxes or [[2677: Two Key System|other things]]). Which is not to say that a specific M-of-N puzzle (where 1<M<N) might not need a ''little'' bit of thought to actually design and implement, but there's no obvious reason why all such combinations shouldn't be nicely doable. [[Special:Contributions/172.69.79.165|172.69.79.165]] 14:56, 23 November 2024 (UTC)
:Can we first confirm that the M-of-N Encryption was what Randall was referencing in the first place? [[Special:Contributions/172.71.154.140|172.71.154.140]] 03:17, 24 November 2024 (UTC)
::No, first confirm that this is what the explanation treats as what Randall was referencing. As it was, "complicated lock mechanics" and/or "magic" were suggested as the only ways of doing this, when this (or what we thought this was) just needs a little thought and N bike-locks suitably entangled. [[Special:Contributions/172.70.58.45|172.70.58.45]] 13:17, 24 November 2024 (UTC)
:I'm glad someone else chimed in on this, because it is definitely ''not'' difficult to require unlocking of multiple discrete locks! I can't even figure out why one might think it would be? [[User:ProphetZarquon|ProphetZarquon]] ([[User talk:ProphetZarquon|talk]]) 15:55, 24 November 2024 (UTC)

"other polyhedral dice, with the number of faces denoted by dX (e.g., d10 is a 10-sided die, with numbers from 1 to 10 on it)." - the d10 may be a poor choice as exemplar here; Back in the last century, when I was playing D&D, d10 were typically (and uniquely) numbered 0-9, not 1-10. This may no longer be the case, and I may be showing my age, but if it is still the norm, the d8 or d20 might be a better choice of example. [[Special:Contributions/172.68.210.6|172.68.210.6]] 02:40, 24 November 2024 (UTC)
:Typically, I've only seen 0-9 d10s, as part of a "d100" dice pair, with one reading 0-9 & the other reading 0⁰-9⁰... Single d10, mostly seem to come in 1-10? Maybe it depends which reseller one shops at... [[User:ProphetZarquon|ProphetZarquon]] ([[User talk:ProphetZarquon|talk]]) 15:49, 24 November 2024 (UTC)
::They are usually numbered 0-9, but the 0 represents 10, since writing 10 would require that face to have a different font size. It is still a d10, since the die has ten sides, and still cannot roll at 0. The d100 variant does the same thing with 100, but for the added reason that the 00 face actually does mean 0 when the other die rolls a 1-9. This is the convention, so a die that actually writes 10 on it instead of 0 will be rare. [[User:Stardragon|Stardragon]] ([[User talk:Stardragon|talk]]) 23:14, 24 November 2024 (UTC)

You've all been nerd-sniped. [[User:CalibansCreations|'''Caliban''']] ([[User talk:CalibansCreations|talk]]) 10:53, 24 November 2024 (UTC)

Combinatorics degree? Does such a degree really exist? --[[Special:Contributions/162.158.130.37|162.158.130.37]] 17:19, 24 November 2024 (UTC)
:There are degrees for all kinds of things. A quick search reveals a number of "Combinatorics" or "Combinatorics and <Foo>" (e.g. "Optimisation") degrees. Some of them are marked as Masters degrees, and I haven't dug into the others to see if there are any 'pure' undergraduate ones (apart from anything else, I know there are crucial differences between the structures and scopes of UK and US 'degree courses' to consider, in particular), but there seems to be representation on both sides of the Atlantic (and elsewhere, e.g. Oceana).
:At the very least, it could be a selected specialised segment of an even wider mathematical degree course, or a cross-disciplinary one (like my own, which was part under Physics and part under Computing, but could have included a Stats-based element). [[Special:Contributions/162.158.74.49|162.158.74.49]] 19:07, 24 November 2024 (UTC)
::So "Combinatorics and <Foo>" would be meta-combinatorics, since it is combining something with something else. :) [[User:RandalSchwartz|RandalSchwartz]] ([[User talk:RandalSchwartz|talk]]) 20:19, 28 November 2024 (UTC)
:::I shall do my degree in "Combinatorics, Selectivity, Comparison, Decision Making and/or Cross-Designation (Choose Any Three)"... [[Special:Contributions/172.70.90.5|172.70.90.5]] 21:28, 28 November 2024 (UTC)

I'm trying this on my DM. -[[User:Psychoticpotato|P?sych??otic?pot??at???o ]] ([[User talk:Psychoticpotato|talk]]) 15:11, 25 November 2024 (UTC)

Can someone put into the Explanation the current details regarding the nature of cursed arrows, in whatever edition of DnD we're currently up to. (8th? I've lost track.) In different DnD-like media, I know that it can act somewhat negatively (reduces aim accuracy) or even outright problematic (it curses the person loosing the projectile; or even renders the bow otherwise useless, as analogue to a cursed weapon), or else reduces/inverts the damage (breaks easier, or essentially acts like a thrown beneficial potion to increase health/strength/stamina/etc of the target). I assume that it one of these, from the assumption that the player desires a "good enough" roll to avoid. On the other hand, cursed projectiles could be treated akin to poisoned arrows or vengeful weapons in doing more, better or more targeted damage (in which case it's a powerful aid, the archer is instead taking a chance of using up a stock of 'special arrows', perhaps in line with not knowing whether their foe ''needs'' that extra degree of offensive power). But, at least from the explaining text's approach to dice-roll results, that doesn't exactly mesh with the typical "higher is better" rolling mantra. [[Special:Contributions/172.70.86.129|172.70.86.129]] 22:43, 25 November 2024 (UTC)

I don't think making an M-of-N mechanism with physical locks would be "extremely cumbersome". For example you could have a bolt that must be drawn back to open the mechanism, with several padlocks over it, where the shackle of each padlock blocks the motion of the bolt, such that the distance you can draw the bolt is proportional to how many padlocks are removed. Removing any m of the n padlocks gives you enough range of motion to open the mechanism.
[[Special:Contributions/172.71.154.224|172.71.154.224]] 23:17, 27 November 2024 (UTC)

A DM with a degree in Combinatorics would be unlikely to find this annoying.[[Special:Contributions/162.158.62.245|162.158.62.245]] 05:30, 30 November 2024 (UTC)

With up to three D&D dice, it is impossible to achieve 2/9 exactly. The closest you can get is with d6 + 2d10x10 >= 126 (where d10x10 denotes the tens die, ranging from 00 to 90) yielding a probability of 133/600 = 0.2216667. [[User:Vandof|Vandof]] ([[User talk:Vandof|talk]]) 06:27, 30 November 2024 (UTC)

3009: Number Shortage

2024-11-12T21:05:54Z

Vandof: /* Explanation */

{{comic
| number = 3009
| date = November 8, 2024
| title = Number Shortage
| image = number_shortage_2x.png
| imagesize = 284x269px
| noexpand = true
| titletext = "10 minutes ago we were down to only 2 0s!" "How many do we have now?" "I ... don't know!!"
}}

==Explanation==
{{incomplete|Created by a BOT WITH 11 0S AND 100 1S. NO, WAIT... - Please change this comment when editing this page. Do NOT delete this tag too soon.}}
This comic presents a situation where the ability to use numbers is a limited resource. Even quantifying how many numbers are left uses up some of those numbers when stating the results.

In real life, being able to write or say digits is not a limited resource.{{cn}} However, the comic does parallel the {{w|look-and-say sequence}} as well as many {{w|Math Blaster Episode I: In Search of Spot|educational video games}} for young children where numbers and mathematical concepts are treated as living people or factory goods, in order to give some sort of story or context to the math-related activities.

The comic conflates numbers with decimal digits. So when [[Miss Lenhart]] says "15 2s and 12 3s", that uses up two 2s (one in "2s" and one in "12") and one 3 (in "3s"). She adjusts the counts as she's speaking, so when she says "13 2s", that uses up another 3, leaving only 10 3s as she's completing the sentence.

In the title text, she uses the last two 0s when saying that they had two 0s left, so now they have no more 0s. But she can't use the number 0 to describe this situation because they're now out of them.

It is unknown where the extra 0 necessary to say "10 3s" came from.

Miss Lenhart could have taken a different approach by saying "14 2s and 11 3s", which would be accurate once it has been said.

Jokes with a similar theme been made about letters, such as shortages of vowels (and later consonants) in {{w|The Onion}}'s [https://web.archive.org/web/20020124120633/www.theonion.com/onion2816/vowels2816.html "Clinton Deploys Vowels to Bosnia"].

===Continuation===

A continuation of the pattern would go:

* "We have only 15 2s and 12 3s left."
* "No, wait, 13 2s and 10 3s."
* "No, wait, 12 2s and 9 3s."
* "No, wait, 10 2s and 8 3s."
* "No, wait, 9 2s and 7 3s."
* "No, wait, 8 2s and 6 3s."
* "No, wait, 7 2s and 5 3s."
* "No, wait, 6 2s and 4 3s."
* "No, wait, 5 2s and 3 3s."
* "No, wait, 4 2s and 1 3."
* "No, wait, ? 2s and 0 ?s."

At that point, having used up the last 3 at the end of the previous line, Miss Lenhart would lack the necessary 3s to articulate that there are "3 2s and 0 3s."

* "No, wait, 2 2s and 0 ?s."
* "No, wait, 0 ?s and 0 ?s."

Or perhaps at this point, she might just say "We have run out of some digits," since she can no longer articulate which ones or, indeed, how many.

==Transcript==
:[Miss Lenhart is standing on the left, facing Cueball and Megan on the right.]
:Miss Lenhart: The Math Department number shortage is getting worse. We have only 15 2s and 12 3s left.
:Miss Lenhart: No, wait, 13 2s and 10 3s.
:Miss Lenhart: No, wait...

{{comic discussion}}

[[Category:Comics featuring Miss Lenhart]]
[[Category:Comics featuring Cueball]]
[[Category:Comics featuring Megan]]
[[Category:Math]]
[[Category:Comics with lowercase text]]

1570: Engineer Syllogism

2024-06-16T04:23:30Z

Vandof: /* Transcript */ Changed "an" to "a"

{{comic
| number = 1570
| date = August 28, 2015
| title = Engineer Syllogism
| image = engineer_syllogism.png
| titletext = The less common, even worse outcome: "3: [everyone in the financial system] WOW, where did all my money just go?"
}}

==Explanation==
A {{w|syllogism}} is a {{w|logic|logical}} argument where two or more propositions lead to a conclusion through {{w|deductive reasoning}}. For example, one of the best-known syllogisms is:
#All men are mortal
#Socrates is a man
#Therefore, Socrates is mortal

In this comic, [[Cueball]] is an engineer who is attempting to make the following syllogism:
#I am good at understanding "numbers" (i.e., mathematics)
#The stock market is made of numbers
#Therefore, I am good at understanding the stock market

Since most engineers are purportedly good at math, proposition 1 seems to be true. It is also loosely true that the {{w|stock market}} is made of numbers, but only in the sense that every system can be given a post-hoc numeric characterization; the dynamics of the stock market are primarily human-driven. In this comic Cueball thinks that his skill at math will help him beat the stock market. Little does he know that the system can be unpredictable, so he ends up losing money as the financial instrument he's invested in loses value. This is due to the financial markets being largely controlled by humans making emotional decisions and not some calculable reason or logic.

High frequency trading does make use of computer software to determine trades (and thus is a lot closer to being "just numbers") but being successful relies on direct low-latency access to financial exchanges that an individual can't get access to. Many engineers (generally software and computer) work at these companies but wouldn't be able to make money trading on their own. Fundamental analysis is also a number-oriented way to determine the value of a company (and thus whether the current price of a stock is good or bad) and can be done by an individual, but requires making qualitative decisions on what data to use and how to do the analysis so it is not "just numbers".

Even if the propositions "I am good at understanding numbers" and "The stock market is made of numbers" were true in Cueball's interpretation, Cueball would still be wrong to conclude that "I am good at understanding the stock market": this would be a {{w|fallacy of the undistributed middle}} (with the first premise being more accurately stated as "I'm good at understanding things made of numbers") and a {{w|fallacy of composition}} (with the implicit third premise "if I'm good at understanding the components of a system, then I'm good at understanding the system"). The problem is that proposition 1 seems to say "I am good at understanding all math". However, the "all" is not present, so Cueball may not necessarily understand the math underlying the stock market.

This comic is also related to the 1998 movie {{W|Pi (film)|Pi}} where the main character repeats to himself several times his assumptions that the world is all numbers, and thus he, a great mathematician, should be able to predict the stock market, which is all numbers. He believes that maybe his work on patterns in pi will provide some deeper insight into the patterns in the stock market, a project that drove his mentor crazy and may in fact be making his computer self-aware.

The title text talks of the scenario where it was Cueball who causes everyone involved in the financial system to lose their money. This could refer to a scenario in which Cueball figures out a way to extract large quantities of money from the stock market, causing a sudden, major decline in everybody else's wealth, or that his involvement has caused literally everyone, including his own, stock market assets to lose their value. This is possible since there is no conservation of value for the stock market. The value of a particular stock is determined by a majority that is willing to trade it at a given price.

The release date of this comic makes it highly likely that it refers at least in part to the {{w|2015 Chinese stock market crash}} which largely affected most other world financial markets, particularly during the week of August 24–28, during which this comic was published.

Two, less likely, interpretations of the title text have been suggested:
#It could also be understood as if everyone makes the fallacy of Cueball and this leads to a much worse global situation - i.e. a stock market crash.
#Alternatively, Cueball could cause a global stock market crash if he is an engineer responsible for vital stock-market-related software and/or hardware. An example of a situation where the action of engineers was implicated in just such a crash is the {{w|2010 Flash Crash}}. High-frequency quantitative trading, which relies more on financial technology engineering than sophisticated financial knowledge, was heavily involved in this particular crash.

This scenario has been mentioned before, in the title text of [[592: Drama]].

A similar fallacy is presented in [[2933: Elementary Physics Paths]].

==Transcript==
:[A white frame with text inside an underbrace and an overbrace.]
:An engineer syllogism

:[Cueball is at his desk in front of his computer, with his hands on his knees, thinking.]
:Cueball (thinking): 1: I am good at understanding numbers.

:[Cueball takes one hand to his chin, still thinking.]
:Cueball (thinking): 2: The stock market is made of numbers.

:[Cueball lifts both arms from his legs, still thinking.]
:Cueball (thinking): 3: Therefore I– '''''Wow''''', where did all my money just go?

{{comic discussion}}

[[Category:Comics featuring Cueball]]
[[Category:Computers]]
[[Category:Math]]
[[Category:Logic]]
[[Category:Stock Market]]
[[Category:Engineering]]