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A fast-food restaurant sells chicken in orders of 6, 9, and 20. What is the largest number of pieces of chicken you cannot order?
The right answer is: 43
After 6, all numbers divisible by 3 can be ordered. After 26, all numbers divisible by 3 when subtracted by 20 can be obtained. After 46, all numbers divisible by 3 when subtracted by 40 can be obtained. After 46, all numbers fit into one of these 3 categories, so all numbers can be obtained. 43 is the last number that doesn't fall into one of these categories (44 = 20 + 6 * 4, 45 = 6 * 6 + 9).
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