Part 1 Part 2 Part 3 Part 4 Part 5 Part 6

 Sudoku Course:    

Welcome to Course in Sudoku

Part 6

Tie-breaker using Ariadne’s thread

Ariadne’s thread permits backtracking - that is, reversing earlier decisions and trying alternatives.

According to the Greek legend Ariadne helped Theseus - a young man who volunteered to kill the Minotaur - by giving him a sword and a ball of thread, so that he could find his way out of the Minotaur's labyrinth by following the thread back.

Using the tie-breaker method any Sudoku puzzle can be solved. The Sudoku Instructions program makes it easy to use this method. Tie-breaker can be applied if following full candidate reduction there is still no single candidate anywhere in the puzzle.

In this puzzle the candidates cannot be reduced further using the methods we have described. There is also not any single candidate - neither hidden nor isolated. So you can apply the tie-breaker method using Ariadne’s thread.

In a square with only two candidate digits left you choose one of them. In square B1 there are two candidate digits. You can chose one of them e.g. Digit 2.

The chosen digit 2 is displayed in red color so you easily can see that this digit is chosen among two or more candidates. Then you proceed as usual in solving the puzzle. There are now single candidates so you can easily continue solving the puzzle. There is an isolated single candidate in square G1. Inserting the digit in the square we arrive at the following stage.

The new digit and the following digits you place on the board will be in violet color. In this way you can easily identify the thread of digits ("Ariadne's thread") back to the tie-breaker digit shown in red.

You proceed by finding single candidates. The next steps may look like this:

Now you see a problem: there is no candidate left for square E5. This means that the selection in square B1 of digit 2 as the tie-breaker was wrong. We therefore need to go back stepwise until we reach that square. In that square we select the other candidate digit (1), which must be the right digit, see below:

Now we can proceed solving the puzzle by finding single candidates. That way we can solve the puzzle completely to arrive at this final solution:

In extremely difficult Sudoku-puzzles it may sometimes be necessary to use tie-breaker more times. If an error arises - for example that in a given square there is no longer any candidate left - you go stepwise back to the latest red digit and in that square try the other candidate digit. If this still leads to an error, you will need to step further back to the previous red digit and in that square try the other candidate digit and so on. When you can place all digits without any error, the right solution has been found.

Maximum candidate reduction

The Sudoku Instructions Program can perform a maximum candidate reduction - in a single step - using its built-in methods. This is a very powerful feature. Consider this sudoku puzzle:

The number of candidates is rather big with too many possibilities for placing the digits. After maximum candidate reduction the puzzle will be much simpler to solve, as there are now many obvious or isolated singles on the board:

Complete computer solving of even the most difficult sudoku puzzle

Using the Sudoku Instructions Program you can let the program solve any sudoku puzzle immediately, see below:

Print sudoku puzzles

Using the Sudoku Instructions program you can print sudoku puzzles of any difficulty with 6 puzzles fitting on an A4 or legal page.

Thus you do not anymore need to buy sudoku puzzle books or magazines.  

This is nice if you want to solve sudoku puzzles without using your computer.

This ends the sudoku course. If you have not yet bought the Sudoku Instructions Program you can buy it here.

Happy Sudoku Solving!

© Sudoku Instructions Programming Unit - All rights reserved