A different angle: can you solve the six dollar game?

At homecoming this year, we gave alumni the opportunity to experience Math 135 class all over again. They learned from award-winning teachers and even tested their skills with a pop-quiz. Participants had a blast—and it reminded us how much Mathies of all ages love solving puzzles.

So we’re bringing back a feature from the old Math Ties (our alumni newsletter when it was just a print publication): A “Different Angle” was a regular column that gave alumni a chance to solve problems created by the Centre for Education in Mathematics and Computing (CEMC).

Below is a new problem for your enjoyment. Give it a try and send us your answers at mathalumni@uwaterloo.ca. We’ll publish the solution in our next issue along with a new problem.

A two-player game has players alternating turns removing coins from three piles. At the beginning of the game, the first pile contains coin, the second pile contains coins, and the third pile contains coins. Players take turns removing one or more coins from any one pile. On their turn, a player can remove from one coin to all of the coins in a particular pile. The player who removes the last coin wins the game.

Jessie and Jason play this game. Jessie goes first. Jason claims that no matter what Jessie does on his turn, that Jason can win by following his winning strategy. Describe Jason’s winning strategy.

Over the last few years, teachers have asked us to expand our resources for Grade 4, 5 and 6 mathematics classrooms. We’re excited to share that the CEMC’s Grade 4/5/6 Mathematics Courseware is now live!

We offer our courseware free of charge, so that all students can benefit. Your financial support makes this possible. Consider making a gift to the CEMC and igniting a passion for math and computing in the next generation.