I've spent the last three days writing code for other things, so I'm just tackling the McNuggets now. :)

Problem 1:

6a,9b,20c = n
2,2,1 = 50
1,5,0 = 51
2,0,2 = 52
1,3,1 = 53
0,6,0 = 54
1,1,2 = 55

If you add 6 to those totals, you get 56,57,58,59,60,61.
If you add 6 to those totals, you get 62,63,64,65,66,67.

Problem 2:

So basically, once the condition is true for any run of six, it's true for that run of six + 6, which works out to every number greater than the start of the first run of six. If it were true for a run of nine, it would also be true for that run of nine + 9, etc.