**ERIC Number:**EJ779067

**Record Type:**Journal

**Publication Date:**2007

**Pages:**2

**Abstractor:**ERIC

**Reference Count:**2

**ISBN:**N/A

**ISSN:**ISSN-0045-0685

Sudoku

de Mestre, Neville

Australian Mathematics Teacher, v63 n4 p6-7 2007

In this article, the author discusses Sudoku--a logic puzzle that has appeared in many newspapers in recent years. In its introductory form it consists of a 9x9 grid in which the digits 1 to 9 inclusive are each to be placed nine times in the 81 separate cells of the grid. Each row and each column may not have any digit repeated. If these were the only rules, then the solved puzzle would be called a Latin square. This name was invented by the Swiss mathematician Leonhard Euler (1707-1783) who first created one on a 3x3 grid using the Latin numeral characters I, II and III. Furthermore, accompanying explanation of the rules of Sudoku in many newspapers claims that solving Sudoku requires no mathematics. However, this is an incorrect statement, for although no calculations seem to be required, the solution of a Sudoku puzzle may require the use of logical reasoning, deduction, and "reductio ad absurdum" techniques which are all part of the rich tapestry of mathematics. Sudoku has an extra constraint compared with a regular 9x9 Latin square. Each of the nine non-overlapping 3x3 sub-grids along the edges and in the centre of the larger grid must also contain the digits 1 to 9 without repetition. To enable a Sudoku puzzle to be solved, particular digits or clues are fixed in place in some cells at the start. The number of these varies, but they should be placed so that the solution is unique. At this stage no one has created a solvable 9x9 Sudoku puzzle with fewer than 17 given clues, but this lower limit has not been proved mathematically. (Contains 3 figures.)

Descriptors: Logical Thinking, Mathematical Concepts, Mathematics Skills, Mathematical Logic, Puzzles, Problem Solving

Australian Association of Mathematics Teachers (AAMT). GPO Box 1729, Adelaide,5001, South Australia. Tel: +61-8-8363-0288; Fax: +61-8-8362-9288; e-mail: office@aamt.edu.au; Web site: http://www.aamt.edu.au

**Publication Type:**Journal Articles; Reports - Descriptive

**Education Level:**N/A

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A