# Problems to Ponder (July edition)

Welcome to this month’s edition of Problems to Ponder! Pose them in your classroom as a challenge or try them out yourself. Have an interesting solution? Send it to thevariable@smts.ca for publication in a future issue of The Variable, our monthly periodical.

The sixth cent

You toss a fair coin 6 times, and I toss a fair coin 5 times. What is the probability that you get more heads than I do?

Adapted from Barbeau, E. J., Klamkin, M. S., & Moser, W. O. J. (1995). Five hundred mathematical challenges. USA: The Mathematical Association of America.

Dueling dice

Consider the following four dice, which have the following numbers on their faces:

• Red : 0, 1, 7, 8, 8, 9
• Blue: 5, 5, 6, 6, 7, 7
• Green: 1, 2, 3, 9, 10, 11
• Black: 3, 4, 4, 5, 11, 12

The dice are used to play the following game for two people. Player 1 chooses a die, then Player 2 chooses a die. Then, each player rolls their die. The player with the highest number showing gets a point. The first player to get 7 points wins the game. If you are Player 1, which die should you choose? If you are Player 2, which die should you choose?