Chicken Lumps riddle?

Question

At a certain fast food chain, you can buy Chicken Lumps in quantities of 6, 9, or 20. So you can buy 21 Lumps (= 2x6 + 9), but you can't buy 5, 19, or 22.

What is the largest number of Chicken Lumps you CAN'T buy, and why?

Answer 1

The answer is 43. The key to solving this is to notice that two of the numbers are multiples of 3, while the third is two more than a multiple of 3. So, the smallest number you can make that is 1 more than a multiple of 3 is 20 + 20 = 40.

Now try adding three to 40 a few times. 40 + 3 = 43 is a solution (since you can't get 3 out of the 6 or 9), but not 40 + 6, 40 + 9, 40 + 12 = 40 + 6 + 6, etc. So, 43 has to be the largest number.