The September issue of The College Mathematics Journal is devoted to articles about puzzles and games. The games discussed include Set, Mancala, and Chomp. Puzzles attacked include chess on a triangular, honeycomb board; Instant Insanity II, and Boggle Logic Puzzles.
Problems and Solutions challenge readers and Media Highlights keep them well-informed, and, finally, there is a Sudoku to solve: a Tetris Sudoku courtesy of Philip Riley and Laura Taalman.—Michael Henle
Vol. 44, No. 4, pp.258-344.
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Sets, Planets, and Comets
Mark Baker, Jane Beltran, Jason Buell, Brian Conrey, Tom Davis, Brianna Donaldson, Jeanne Detorre-Ozeki, Leila Dibble, Tom Freeman, Robert Hammie, Julie Montgomery, Avery Pickford, and Justine Wong
Sets in the game Set are lines in a certain four-dimensional space. Here we introduce planes into the game, leading to interesting mathematical questions, some of which we solve, and to a wonderful variation on the game Set, in which every tableau of nine cards must contain at least one configuration for a player to pick up.
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JSTOR: http://dx.doi.org/10.4169/college.math.j.44.4.258
Instant Insanity II
Tom Richmond and Aaron Young
Instant Insanity II is a sliding mechanical puzzle whose solution requires the special alignment of 16 colored tiles. We count the number of solutions of the puzzle’s classic challenge and show that the more difficult ultimate challenge has, up to row permutation, exactly two solutions, and further show that no similarly-constructed puzzle can have a unique ultimate solution.
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JSTOR: http://dx.doi.org/10.4169/college.math.j.44.4.265
Mancala Matrices
L. Taalman, A. Tongen, B. Warren, F. Wyrick-Flax, and I. Yoon
This paper introduces a new matrix tool for the sowing game Tchoukaillon, which establishes a relationship between board vectors and move vectors that does not depend on actually playing the game. This allows for simpler proofs than currently appear in the literature for two key theorems, as well as a new method for constructing move vectors. We also explore extensions to Mancala, a popular two-player sowing game.
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JSTOR: http://dx.doi.org/10.4169/college.math.j.44.4.273
Proof Without Words: Squares Modulo 3
Roger B. Nelsen
Using the fact that the sum of the first n odd numbers is n2, we show visually that n2 ≡ 0 (mod 3) when n ≡ 0 (mod 3), and n2 ≡ 1 (mod 3) when n ≡ ±1 (mod 3).
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JSTOR: http://dx.doi.org/10.4169/college.math.j.44.4.283
Chomp in Disguise
Andrew MacLaughlin and Alex Meadows
We investigate Chomp, a game popular with chocolate lovers, and various other combinatorial games associated with it.
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JSTOR: http://dx.doi.org/10.4169/college.math.j.44.4.284
Tetris Sudoku
Philip Riley and Laura Taalman
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JSTOR: http://dx.doi.org/10.4169/college.math.j.44.4.292
Boggle Logic Puzzles: Minimal Solutions
Jonathan Needleman
Boggle logic puzzles are based on the popular word game Boggle played backwards. Given a list of words, the problem is to recreate the board. We explore these puzzles on a board and find the minimum number of three-letter words needed to create a puzzle with a unique solution. We conclude with a series of open questions.
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JSTOR: http://dx.doi.org/10.4169/college.math.j.44.4.293
Counting Knights and Knaves
Oscar Levin and Gerri M. Roberts
To understand better some of the classic knights and knaves puzzles, we count them. Doing so reveals a surprising connection between puzzles and solutions, and highlights some beautiful combinatorial identities.
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JSTOR: http://dx.doi.org/10.4169/college.math.j.44.4.300
Domination and Independence on a Triangular Honeycomb Chessboard
Joe DeMaio and Hong Lien Tran
We define moves for king, queen, rook, bishop, and knight on a triangular honeycomb chessboard. Domination and independence numbers on this board for each piece are analyzed.
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JSTOR: http://dx.doi.org/10.4169/college.math.j.44.4.307
Are Stupid Dice Necessary?
Frank Bermudez, Anthony Medina, Amber Rosin, and Eren Scott
A pair of 6-sided dice cannot be relabeled to make the sums 2, 3, . . ., 12 equally likely. It is possible to label seven, 10-sided dice so that the sums 7, 8, . . ., 70 occur equally often. We investigate such relabelings for pq-sided dice, where p and q are distinct primes, and show that these relabelings usually involve stupid dice, that is, dice with the same label on every face.
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JSTOR: http://dx.doi.org/10.4169/college.math.j.44.4.315
Proof Without Words: The Area of an Inner Square
Marc Chamberland
What is the area of the (inner) square obtained by slicing the corners off a larger square? This visual proof avoids algebra by considering the area of a parallelogram.
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JSTOR: http://dx.doi.org/10.4169/college.math.j.44.4.322
CLASSROOM CAPSULE
A Power Rule Proof without Limits
Colin Day
Without using limits, we prove that the integral of xn from 0 to L is Ln +1/(n + 1) by exploiting the symmetry of an n-dimensional cube.
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JSTOR: http://dx.doi.org/10.4169/college.math.j.44.4.323
PROBLEMS AND SOLUTIONS
Problems 1006-1010
Solutions 981-985
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JSTOR: http://dx.doi.org/10.4169/college.math.j.44.4.325
REVIEWS
Encyclopedia of Mathematics and Society, Sarah J. Greenwald and Jill E. Thomley eds., Salem Press, 2011, 1191 pp., ISBN 9781587658440. $395.
Reviewed by Gizem Karaali
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JSTOR: http://dx.doi.org/10.4169/college.math.j.44.4.332
MEDIA HIGHLIGHTS