## Absolute Sum

#### Problem

For all real numbers, $|x|$ is defined as the absolute value of $x$; for example $|4.2| = 4.2$ and $|-7| = 7$.

Given that $x$ and $y$ are integer, how many different solutions does the equation $|x| + 2|y| = 100$ have?

Problem ID: 292 (03 Oct 2006) Difficulty: 3 Star