Chicken McNugget Theorem.

Algebra Level 3

In a game of Bash Bing, a player can score 6 points, 9 points, or 20 points. What is the greatest possible integer that a player cannot achieve in a game of Bash Bing?

31 59 63 43 47 61

2 solutions

Kyle T
May 23, 2019

First lets eliminate any of the answer options that we can actually create:
(20 * 0) + (9 * 1) + (6 * 9) = 63
(20 * 1) + (9 * 1) + (6 * 3) = 47
(20 * 1) + (9 * 1) + (6 * 5) = 59
(20 * 2) + (9 * 1) + (6 * 2) = 61

That leaves 2 options, 31 and 43; the higher of which is our answer: 43

A Former Brilliant Member
May 23, 2019

I computed all possible sums of scores, including zero of each type, using 666 as an upper limit. I then computed the complement of that set with an universe of the integers from 0 to 666. I then computed the maximum of the complement set. That maximum is 43. See Postage Stamp Problem / Chicken McNugget Theorem

Chicken McNugget Theorem.

2 solutions

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