I Just Love Chicken So Much
Riddle: 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 from this restaurant?
Answer: 43. After 6 all numbers divisible by 3 can be ordered (because they can all be expressed as a sum of 6's and 9's). After 26, all numbers divisible by three when subtracted by 20 can be obtained. After 46, all numbers divisible by three 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).
Source: https://www.riddles.com/index.php/5886
