# 953: 1 to 10

1 to 10 |

Title text: If you get an 11/100 on a CS test, but you claim it should be counted as a 'C', they'll probably decide you deserve the upgrade. |

## Explanation

The binary numeral system refers to a counting system in base-2, which uses only the digits 0 and 1, as opposed to the more familiar base-10 decimal system, which uses the digits 0 through 9. In this case, the scale of 1 to 10 is using binary, so in decimal it would be a scale of 1 to 2. Since 4 in binary is "100" it doesn't fit into the range "1" to "10" in a binary system. And Megan doesn't even know the number "4" because she's only working on the binary system, this character does not exist for her.

It is also possible that Megan is using base-3, which also doesn't use a '4' but counts 1, 2, 3, 10, etc.

The title text uses a similar joke. Since test scores are usually written as either a letter grade or a percentage, 11 correct questions out of 100 would be a failing score in decimal notation. However, 11/100 in binary translates to 3/4 in decimal, which would be 75%, accepted in most classes as a 'C' grade.

## Transcript

- Megan: On a scale of 1 to 10, how likely is it that this question is using Binary?
- Cueball: ...4?
- Megan: What's a 4?

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# Discussion

One of correct answers is P = 1 + 1 - |sgn(10 - 1 - 1)|

(|x| is absolute value of x, sgn(x) is 1 when x > 0, 0 when x = 0, and -1 when x < 0)

If 10 = 1 + 1, then P = 10 - |sgn(0)| = 10 - |0| = 10

If 10 > 1 + 1, then P = 1 + 1 - |sgn(10 - 1 - 1)| = 1 + 1 - |1| = 1

If 10 < 1 + 1, then P = 1 + 1 - |sgn(10 - 1 - 1)| = 1 + 1 - |-1| = 1

So P is 10 iif the question was is in binary, and 1 iif it was not in binary.

93.73.186.104 16:26, 6 February 2013 (UTC)

- The absolute value is unnecessary. When is 10 ever less than 1+1?108.162.219.202 20:28, 3 January 2014 (UTC)

I don't think the explanation is right, I mean i don't know binary but i don't think the joke is that he's saying a 4 as in 100% Lackadaisical (talk) 00:23, 7 November 2013 (UTC)

- A 4 is not 100%, but a 3/4 is always 75%. 108.162.212.206 22:47, 26 January 2014 (UTC)

1.(1) is the best answer I've got Halfhat (talk) 11:53, 5 April 2014 (UTC)

"How likely" it is? As everyone knows, "every base is base 10", since every base number in its own numbering system is written as "10" (2 is 10 in binary, 16 is 10 in hex and so on). So that question could be in EVERY number system possible. I suppose the probability is then 1 over an infinite number of systems, then very unlikely, so I'd say (as 0 is not in the range of possible answers) the answer is 1. Which, incidentally, is also an acceptable answer for every system. If we want instead to take into account that Megan doesn't know what a 4 is, the possibilities are only base 2, 3 and 4. So the likeliness is 1/3, which corresponds anyway to 1 in those number systems. --108.162.229.31 14:05, 3 June 2014 (UTC)

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