Buying Chicken Nuggets

Problem: You can go to a fast food restaurant to buy chicken nuggets in 6-pack, 9-pack or 20-packs. is there such a number N, such that for all numbers bigger than or equal to N, you can buy that number of chicken nuggets?

Solution:

Here's another way of looking at it:

 1  2  3
4  5  6
7  8  9
10 11 12
13 14 15
16 17 18
19 20 21
22 23 24
25 26 27
28 29 30
31 32 33
34 35 36
37 38 39
40 41 42
43 44 45
(and so on, to infinity)

You can get any number in the right column except 3 by adding 6s and 9s. So cross out the entire right column except 3. You can also add 20 to any crossed-out number and cross that number out. So cross out everything in column two below and including 26. Finally, by the same logic you can add 20 to the crossed-out numbers in column 2 and thereby cross out everything in column one below and including 46.

The largest number that's left over is 43. Incidentally, cross out 20 and 40 and your map is complete.