Please feel free to play around with some of the math puzzles below. While we may or may not explore these particular puzzles at our math circles, you can stretch your problem-solving muscles with these, and if you enjoy yourself, then our MTC is certainly for you!
1. Dividing a Square: If you are given a square of an arbitrary size, you can subdivide it into 4 smaller squares (by cutting it in half, and then in half again). For what value of n can you subdivide a square into n smaller squares? Are any values of n impossible, and why? Remember, the smaller squares need to be the same size as each other!
2. Counting Zeroes: A factorial is a product of a sequence of consecutive natural numbers, beginning with 1. For example, 5! = 5*4*3*2*1 = 120. How many zeroes are at the end of 100! ? Note: don't try to compute 100! by hand, it is larger than the number of atoms in the observable universe!
3. Balancing the Scales: You have a collection of 50 coins, each weighing a different amount: 1 ounce, 2 ounces, 3 ounces, etc. until your largest 50 ounce coin. Is it possible to divide these coins between two sides of a scale so that the scale balances?
Looking for more math puzzles to explore? Try the Julia Robinson Math Festival website; this is a goldmine of fun problems and activities! JRMF Puzzles Website
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