# How to play Sudoku

Page Contents

## What is Sudoku

Sudoku is a puzzle game similar to Tetris, but the player arranges numbers in the 9×9 grid.

You have to arrange nine digits so that each row, column, and 3×3 box contains every digit only once. The puzzle can be solved quickly with logic. If you are stuck, try looking at the numbers in different rows or columns before returning to pervious steps.

If there are no more numbers that can fit into a row or column then it must contain the number one. If there are still empty spaces in the row or column then there is not enough information available to solve it yet.

For each row, column, and box the sum of all digits should be 45. If there are no digits in a line then it will also have a sum of 45.

Different numbers can share the same lines or boxes without affecting the solution.

The digital root can help find if there is not enough information available to solve the puzzle.

Every number is greater than zero. The digital root is simply the sum of all digits in a number, with no carryover when adding more digits. This means that it is possible for two or more numbers to have the same digital root.

Digital roots are only useful when comparing numbers that share an axis, row or column.

If two or more numbers have the same digital root, then they cannot occupy the same lines or boxes. This is because they would have to sum up to the same amount, but this is impossible. For example, there are only three possibilities of placing four 5s on an empty 9×9 grid:

When comparing two numbers that share an axis, row or column, the number with the larger digital root is greater. If two numbers have the same digital root then they must contain different digits and cannot share lines or boxes.

This means that there are three possible arrangements for three 8s on a 9×9 grid:

All of these arrangements are valid because each one has a different digital root.

This means that when comparing numbers on an axis, row or column the number with the larger digital root will be greater. If two numbers have the same digital root then they must contain different digits and cannot share lines or boxes.

When finding the sum of all digits in a grid it is best to add one number at time.

For example, if there are 8s in the grid (8-2-6) you should sum up all of the individual numbers first (that is 1+2+6=9). Then place the last digit inside the box that has a digital root of 9. If there was no number with a digital root of 9 then the number would have been greater than nine. In this case, the final sum should be 45, because there are no special digital roots in a 3×3 grid.

If you were playing by yourself and had a few minutes to spare you could easily solve a Sudoku puzzle quickly with logic. The following techniques can help if you don’t have a lot of time or you are playing with friends.

## How to play Sudoku

1) Look for a number that can fit into all the rows, columns and boxes. If there is no number that fits in every row, column and box then it cannot be solved yet.

2) Find the largest possible number that still fits into all rows, columns and boxes. If two numbers are possible to be in the same row, column or box then all other numbers must be different.

3) Check if there are any candidates for each of the digits in a set of nine numbers. The sum of these numbers must equal 45 and greater than every number in the set.

4) For each row, column and box try to add up one number at a time. If the sum is greater than 45 then there must be two numbers with the same digital root in that row, column or box.

5) Try adding larger numbers to a line or box first before smaller ones. This can help reduce the amount of candidates and speed up the process.

So this is how to play Sudoku.