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Question

A book is said to have n leaves if it is composed of n pieces of paper. On the other hand, the number of pages is twice the number of leaves because each side of a piece of paper is defined as a page. If the number of pages in a book is 3 more than a multiple of 7, and the number of leaves is greater than 100, then what is the smallest possible number of leaves?

Accepted Answer

Let m be the least possible number of leaves. Then 2m is the least possible number of pages. We know that 2m 3 7 8m 3 4 7 m 12 5 7. So m=5+7a for some positive integer a. The smallest such number greater than 100 is 5+7 14=103.