Session Style: Try a Smaller Problem

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Lockers: An Open-and-Shut Case

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A classic Math Circle problem! At a large high school, there are 10000 lockers. The lockers are numbered, in order, 1, 2, 3, . . . , 10000, and to start, each locker is closed. There are also 10000 students, also numbered 1, 2, 3, . . . , 10000....

Probability

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Some probability problems can be solved by drawing a picture; this approach is sometimes called geometric probability. Other approaches can include experimentation, looking at smaller cases, looking at extreme cases, recursion, or carefully listing possibilities. This session includes ten problems that can be explored alone or in sets, providing material...

Recruiting Change for a Dollar

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How many different ways are there to make change for a dollar? As mathematicians we often search for patterns in a problem. However, for this problem, there is no simple, predictable pattern to build to an answer, encouraging participants to reach outside their comfort zones and ponder alternative strategies in...

Simplex Locks

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A simplex lock is a type of combination door lock that involves pushing-in buttons. Given the set of rules for using a 5-button simplex lock, how many different combinations are there?

The Futurama Theorem

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In the television show Futurama, Professor Farnsworth and Amy decide to try out their newly finished “Mind-Switcher” invention on themselves. When they try to switch back, they discover a key flaw in the machine’s design: it will not allow the same pair of bodies to be used in the machine...