Question

A grocer had some eggs. When he packed them into groups of 4 there were three eggs leftover when he packed them into groups of five there were two left over when he packed them into groups of nine there were no eggs leftover. Find the least number of eggs to grocery had.

Answer 1

The answer has to be a multiple of nine, such as 9, 18, 27, 36, 45.... The number also has to be two more than a multiple of five. Possibilities are 7, 12, 17, 22 and 27. It also has to be three more than a multiple of four, such as 7, 11, 15, 19, 23 or 27. The smallest number in common among all three scenarios is 27, so that is the least number the grocer could have.