In our Good Will Hunting podcast we asked:
What is the highest number of eggs that you CAN'T make, when you have boxes of size 6, 9 and 20?
Turns out this is called the McNuggest number as McNuggets originally came in boxes of this size.
In this case, it turns out that 43 is the largest number you can't make, but how do you prove it?
Well we note that:
44 = 4x6+20
45 = 5x9
46 = 6+2x20
47 = 3x9+20
48 = 8x6
49 = 9+2x20
Since we have 6 consecutive numbers that can all be made from 6, 9 and 20, then every number there after can be made simply by adding an appropriate multiple of 6, e.g. 50 = 44+6, 51 = 45+6, etc.
Simple, no?
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