There are many $a\times b$ rectangular cardboard pieces ($a,b\in\mathbb{N}$ such that $a<b$). It is given that by putting such pieces together without overlapping one can make $49\times 51$ rectangle, and $99\times 101$ rectangle. Can one uniquely determine $a,b$ from this?
Problem
Source: Tournament of Towns,Spring 2002, Junior O Level, P1
Tags: geometry, rectangle, number theory, greatest common divisor, combinatorics proposed, combinatorics