International Mathematical Talent Search
Problem 2/17. Find all pairs of positive integers (m,n) for which .
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 full name and mailing address.
Department of Mathematics
University of Toronto
Toronto, ON M5S 3G3
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