# Sudoku

## How to Play

The objective is to fill a 9×9 grid with digits so that each column, each row, and each of the nine 3×3 sub-grids that compose the grid (also called "boxes", "blocks", "regions", or "sub-squares") contains all of the digits from 1 to 9. The puzzle setter provides a partially completed grid, which for a well-posed puzzle has a unique solution.

## History

The game in its current form was invented by American Howard Garns in 1979 and published by Dell Magazines as "Numbers in Place." In 1984, Maki Kaji of Japan published it in the magazine of his puzzle company Nikoli. He gave the game its modern name of Sudoku, which means "Single Numbers." The puzzle became popular in Japan and was discovered there by New Zealander Wayne Gould, who then wrote a computer program that would generate Sudokus. He was able to get some puzzles printed in the London newspaper The Times beginning in 2004. Soon after, Sudoku-fever swept England. The puzzle finally became popular in the U.S. in 2005. It has become a regular feature in many newspapers and magazines and is enjoyed by people all over the globe.

## Math Concepts

To solve a Sudoku puzzle, one needs to use a combination of logic and trial-and-error. More math is involved behind the scenes: combinatorics used in counting valid Sudoku grids, group theory used to describe ideas of when two grids are equivalent, and computational complexity with regards to solving Sudokus.

When one hears that no math is required to solve Sudoku, what is really meant is that no arithmetic is required. The puzzle does not depend on the fact that the nine placeholders used are the digits from 1 to 9. Any nine symbols would serve just as well to create and solve the puzzles. In fact, mathematical thinking in the form of logical deduction is very useful in solving Sudokus.

You often need more complicated analysis methods to make progress, and sometimes you need to make a guess and proceed, backtracking if the guess results in a conflict.

Looking for patterns and using logic is necessary to solve these puzzles.

## Levels / Grades

Depending on what students are learning about, how they are working with and analyzing the puzzles, and what grade level they are in the DOK levels can range from 1-4.

There is something to learn in all grade levels - mostly 2-8

## Pros/Cons

There are many pros to using Sudoku in classrooms. Getting students to use their conceptual knowledge as well as procedural knowledge is a definite Pro.

Students can use their conceptual knowledge of numbers and the game to find patterns and relationships of how the numbers work together as well as how the procedures and rules with the puzzles restrict certain aspects of the game. With different variations of the puzzle you can help students use the procedures to discover patterns with math, letters, and even algebra.

The cons to this game are that some puzzles are very difficult. It also may be to advanced for some students in the classroom to do, or could take a long time to figure out the entire puzzle, especially if there was a mistake made.