The classic McNugget problem states:
Chicken McNuggets can be purchased in quantities of 6, 9, and 20 pieces. You can buy exactly 15 pieces by purchasing a 6 and a 9, but you can't buy exactly 10 McNuggets. What is the largest number of McNuggets that can NOT be purchased?
The problem can be generalized to one of:
If you have an item that can be purchased in quantities of $a$, $b$, and $c$ ($a < b < c$, $gcd(a,b,c) = 1$), what is the largest integer $N$ of the item that cannot be purchased? (found by integers $x$, $y$, $z$ that satisfy $xa + yb + zc = N$)
In Computer Science class today, we were discussing general ways to solve this problem and one way is to find the smallest sequence of $a$ consecutive numbers that could all be formed by $xa + yb + zc$. Then the largest number that cannot be purchased is one less than the first of the $a$ consecutive numbers.
Our question was: how would you determine the starting point to try sequences of $a$ consecutive numbers? You do not want to start too low, or you will take a long time to find the solution, and you do not want to start too high, or you may miss the solution.