International Mathematical Talent Search

**Problem 2/17**. Find all pairs of positive integers (m,n) for
which m^2 - n^2 = 1995.

**Problem 3/17**. Show that it is possible to arrange in the
plane 8 points so that no 5 of them will be the vertices of a convex
pentagon. (A polygon is *convex* if all of its interior angles
are less than or equal to 180 degrees).

**Problem 4/17**. A man is 6 years older than his wife. He noticed
4 years ago that he has been married to her exactly half of his life.
How old will he be on their 50th anniversary if in 10 years she will
have spent two-thirds of her life married to him?

**Problem 5/17**. What is the minimum number of 3 by 5
rectangles that will cover a 26 by 26 square? The rectangles may
overlap each other and/or the edges of the square. You should
demonstrate your conclusion with a sketch of the covering.

*Solve as many of the problems as you can (you need not solve them all),
and mail your solutions to:*

Professor E. J. BarbeauMake sure that the front page of your solutions contains your

Department of Mathematics

University of Toronto

Toronto, ON M5S 3G3

These problems are made available through the quarterly journal

This page last updated: February 3, 1997

Original Web Site Creator / Mathematical Content Developer: Philip Spencer

Current Network Coordinator and Contact Person: Joel Chan - mathnet@math.toronto.edu

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