jmc

Question

Your friend has an egg collection comprising at least 200 eggs. He wants to store them in dozen-egg containers. After filling as many containers as possible, the last container had 1 egg left over. He then decided to store his eggs in customized baker-dozen-egg containers, where each container can hold 13 eggs. It turns out that, after filling as many of these containers as possible, he still has 1 egg left over. What is the minimum number of eggs that your friend could have?

Accepted Answer

We want the smallest integer x such that x 200 and x gives a remainder of 1 when divided by both 12 and 13. We can write x = 12 13n + 1 = 156n+1, so now we need to find a sufficiently large value of n such that x 200. If n = 1, x = 157, but when n = 2, x = 313. Therefore, your friend has 313 eggs.