*Welcome to this monthâ€™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?

*Adapted from* *Duelling dice.* (n.d.). Retrieved from Mathematics Centre website: http://mathematicscentre.com/taskcentre/046dueld.htm

**Two too many dice**

**
**Suppose you have a clear, sealed cube containing three smaller, indistinguishable six-sided dice. How can you use this three-in-one die to simulate a single, six-sided die? (Bonus: How can you use the three-in-one die to simulate

*two*six-sided dice?)

*Adapted from* Parker, M. [standupmaths]. (2016, April 12). *The three indistinguishable dice puzzle.* Retrieved from https://youtu.be/xHh0ui5mi_E