College Mathematics Journal Contents—September 2013

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