Vol. 7, No. 2, 2014

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Analysis of a Sudoku variation using partially ordered sets and equivalence relations

Ana Burgers, Shelly Smith and Katherine Varga

Vol. 7 (2014), No. 2, 187–204
Abstract

Sudoku is a popular game of logic, and there are many variations of the standard puzzle. We investigate a variation of Sudoku that uses inequalities between cells rather than numerical clues. We begin with an overview of the rules and strategies of the game. We then examine the solvability of an individual m × n block with the use of partially ordered sets, and combine 2 × 2 blocks to form 4 × 4 puzzles.

Keywords
Sudoku, partial order, total order, equivalence relation
Mathematical Subject Classification 2010
Primary: 06A06, 20B30, 91A46
Milestones
Received: 13 December 2012
Accepted: 30 March 2013
Published: 16 November 2013

Communicated by Ann Trenk
Authors
Ana Burgers
University of Minnesota
214 Folwell Hall
9 Pleasant Street, SE
Minneapolis, MN 55455
United States
Shelly Smith
Department of Mathematics
Grand Valley State University
1 Campus Drive
Allendale, MI 49401-9403
United States
Katherine Varga
Department of Mathematics
North Carolina State University
2108 SAS Hall
Box 8205
Raleigh, NC 27695
United States