What is the greatest number of chicken nuggets you cannot order?

Question

At the McClucky's, you can order chicken nuggets in boxes of 6, 9, or 20. By ordering 2 boxes of 6 you can get 12; but you cannot order 13, since no combinations of 6, 9, or 20 added up to 13. What is the greatest number of chicken nuggets that you cannot order?

Answer 1

If you permit multiple purchases, then there is no single answer to this question.

 

For example, 10 boxes of 6 + 10 boxes of 9 + 10 boxes of 20 = 350. In that case, a purchase of 349 will not be possible.

 

When we look at this question, we see that the expression which will give us a total will be x(35) - 1, as long as x is a whole number.