This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

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Found problems: 28

2006 Purple Comet Problems, 10
Tags: geometry , rectangle , 2006
How many rectangles are there in the diagram below such that the sum of the numbers within the rectangle is a multiple of 7? [asy] int n; n=0; for (int i=0; i<=7;++i) { draw((i,0)--(i,7)); draw((0,i)--(7,i)); for (int a=0; a<=7;++a) { if ((a != 7)&&(i != 7)) { n=n+1; label((string) n,(a,i),(2,2)); } } } [/asy]

2006 Purple Comet Problems, 5
Tags: modular arithmetic , 2006
Find the sum of all positive integers less than $2006$ which are both multiples of six and one more than a multiple of seven.

2006 Purple Comet Problems, 6
Tags: 2006
The positive integers $v, w, x, y$, and $z$ satisfy the equation \[v + \frac{1}{w + \frac{1}{x + \frac{1}{y + \frac{1}{z}}}} = \frac{222}{155}.\] Compute $10^4 v + 10^3 w + 10^2 x + 10 y + z$.