Talk:3015: D&D Combinatorics

2024-11-24T17:19:19Z

162.158.130.37: Combinatorics degree?

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.

: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

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)

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.

== Alternative way to calculate the probability of drawing two non-cursed arrows ==

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)
: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)

== The physical difficulties of an M-of-N locking system ==
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)

==Polyhedral Dice==
"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)

== You've all been nerd-sniped. ==

[[User:CalibansCreations|'''<span style="color:#ff0000;">Caliban</span>''']] ([[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)

2874: Iceland

2024-01-18T23:46:08Z

162.158.130.37: /* Explanation */

{{comic
| number = 2874
| date = December 29, 2023
| title = Iceland
| image = iceland_2x.png
| imagesize = 325x454px
| noexpand = true
| titletext = The HVAC bill for installing the Gulf Stream was enormous.
}}

==Explanation==

This comic is a reference to the strange geography of Iceland, owing to the sheer number of notable geographical features in such a small area, leading to the conclusion by Randall that Iceland had to have been created by a committee of various planetary scientists all vying to have their ideas implemented into their 'project', that being Iceland.

The comic depicts a scene of a Cueball giving a presentation to a bunch of members sitting around a table, that being White Hat, Blondie, another Cueball, Megan and Hairbun, in the order left to right. It may have been inspired by Iceland being recently in the news for its {{w|2023 Sundhnúkur eruption|notable volcanic activity}}, although at least this one isn't one of the ones {{w|Eyjafjallajökull|under a glacier}}, so only (currently) causing fairly localised inconvenience.

Noting that being nearer the magnetic pole might more frequently provide you with an aurora, but the more severe (on the {{w|K-index#The Kp-index and estimated Kp-index|Kp index}}) geomagnetic storms invoke their auroral displays at lower latitudes. Once you get a Kp of 5 (out of a theoretical 9), Iceland may be far ''too'' close to the pole to fully appreciate the sight.

A possible alternative viewpoint that can be taken in this comic is about projects that have unrealistic targets (and often fail as a result). The bottom text has already set itself a very unrealistic target by attempting to satisfy 'everyone', even though such a task would be rendered impossible should a single instance of conflicting desires ever occur. In addition, the various ideas that the characters are each vying for to be implemented into the project (that being Iceland) in this comic would each likely require significant resources to accomplish, causing the project requirements to balloon so drastically that meeting its targets would become impossible. This process is often described as {{w|feature creep}}.

{{w|HVAC}} in the title text is jargon for heating, ventilation, and air conditioning. The {{w|Gulf Stream}} is a warm and swift Atlantic ocean current that originates in the Gulf of Mexico and flows through the Straits of Florida and up the eastern coastline of the United States, then veers east near 36 degrees latitude and moves toward Northwest Europe as the North Atlantic Current, providing Iceland with a milder and more liveable climate than would be otherwise expected for its latitude. The electrical costs associated with providing airflow at a certain temperature, over such a vast area would prove incredibly expensive, not to mention the fact that the Gulf Stream is not in fact an artificial phenomenon powered by electricity, but rather a natural one.{{cn}}

==Transcript==
:[Cueball is standing in front of a board and pointing to it with a stick. In front of him is a long table with White Hat, Blondie, another Cueball and Megan sitting on the long side of the table (the same side, the one away from the reader) with Hairbun sitting at the end of the table furthest from Cueball. All are sitting on office chairs and looking at Cueball. On the board there are two figures and some unreadable text. The top figure is an skewed ellipse with some dots inside. There is a label text beneath it. The next large figure depicts an island with a rift going down its middle. The rift extends on either side of the island. There is a label above it. Beneath this there is a box with four lines of unreadable text and above it a heading. Cueball's stick points to the island.]
:Cueball: Okay, we'll make it an island on a mid-ocean ridge to satisfy the mantle people and the oceanographers.
:Cueball-like man: But what about my glaciers?
:Cueball: We can just pile them on the volcanoes.
:Hairbun: Don't forget that it has to be near a pole - I was promised aurora!

:[Caption below the comic:]
:Iceland was designed by a committee of planetary scientists that was trying to satisfy everyone.

{{comic discussion}}

[[Category:Comics featuring Cueball]]
[[Category:Comics featuring White Hat]]
[[Category:Comics featuring Blondie]]
[[Category:Comics featuring Megan]]
[[Category:Comics featuring Hairbun]]
[[Category:Multiple Cueballs]]
[[Category:Volcanoes]]
[[Category:Geography]]
[[Category:Geology]]
[[Category:Engineering]]

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Talk:3015: D&D Combinatorics

2874: Iceland