jmc

Question

There are 54 chips in a box. Each chip is either small or large. If the number of small chips is greater than the number of large chips by a prime number of chips, what is the greatest possible number of large chips?

Accepted Answer

Let s be the number of small chips and l be the number of large chips. From the given information, we have s+l=54 and s=l+p for some prime p. Thus, 2l+p=54. We wish to maximize l, so we must minimize p. Therefore, we set p=2 to get l=26.