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Liar’s Bingo

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From recognizing a pattern to generating terms, to abstracting and making inferences, tasks based on patterns embody the “low-threshold, high-ceiling” trait of good problems. Liar’s Bingo is all about patterns. This session involves recognizing patterns and searching for underlying structure, number theory, numeration, and potentially binary arithmetic. Sometimes, as in...

Locked Out: A Breakout Box Session for Your Circle

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Escape Rooms and “Bomb Disposal” activities are growing in popularity as a form of team building and entertainment. This session blends the two ideas to create a cooperative math activity where the challenge is to solve math problems whose solutions generate combinations to open a locked box. The math problems...

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....

Mathematical Magic for Muggles

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Presented are several easy-to-perform feats that suggest supernatural powers such as telepathy, “seeing fingers,” predicting the future, photographic memory, etc. Each trick uses simple mathematical ideas that allow information to flow effortlessly and sneakily, among them simple, efficient “coding” parity and other invariants symmetry probability One can approach these activities...

One, Two, Three, Four: Building Numbers with Four Operations

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What numbers can you make with 1, 2, 3, and 4, using the operations of addition, subtraction, and multiplication? Work on these problems builds arithmetic fluency and provides opportunities to identify patterns, develop and defend arguments, and create conjectures. This investigation also highlights how thin the boundary is between a...

Optimal Locations of Firehouses (Taxi-cab Metric)

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This session asks participants to expand their notion of “distance,” using a nontraditional taxicab metric instead of the usual Pythagorean notion. Participants are guided to construct the equivalent of “circles” with this new metric and to look at the intersections of multiple such circles. In particular, two firehouses in Gridtown...