At a certain nation-wide fast food chain, you can get chicken nuggets in boxes of 6, 9, and 20. What is the maximum number of nuggets you could ask for such that no combination of the 3 sizes will give you exactly what you wanted?
S = 6s, N = 9s, T = 20s.
S-8, N+1, T+2 -> +1
S-3, T+2 -> +2
S-1, N+1 -> +3
S-6, T+2 -> +4
S-4, N+1, T+1 -> +5
(obviously S+1 -> +6, etc..)
the biggest modification on S is S-8,
so my first guess would be 6*8 - 1 = 47
transformations
