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Sudoku Solver Please report any bugs. Tested in IE, Firefox, Safari and Chrome.
Feedback: Form and User Comments/Questions Here
Candidates can be Edited or Highlighted / Shown
Enter clues or solutions
1 2 3 4 5 6 7 8 9
Check for solved cells   
Show Possibles  
1: Hidden Singles  
2: Naked Pairs/Triples  
3: Hidden Pairs/Triples 
4: Naked Quads 
5: Pointing Pairs  
6: Box/Line Reduction  
Tough Strategies
7: X-Wing  
8: Simple Colouring  
9: Y-Wing  
10: Sword-Fish  
11: XYZ Wing  
Diabolical Strategies
12: X-Cycles  
13: XY-Chain  
14: 3D Medusa  
15: Jelly-Fish  
16: Unique Rectangles  
17: Extended Unique Rect.  
18: Hidden Unique Rect's  
19: WXYZ Wing  
20: Aligned Pair Exclusion  
Extreme Strategies
21: Grouped X-Cycles  
22: Empty Rectangles  
23: Finned X-Wing  
24: Finned Sword-Fish  
25: Altern. Inference Chains 
26: Sue-de-Coq  
27: Digit Forcing Chains  
28: Nishio Forcing Chains 
29: Cell Forcing Chains  
30: Unit Forcing Chains  
31: Almost Locked Sets  
32: Death Blossom  
33: Pattern Overlay Method  
34: Quad Forcing Chains  
"Trial and Error"
35: Bowman's Bingo 

Key
Show Strong (bi-location) links in
Boxes Rows Columns
1 2 3 4 5 6 7 8 9

Please report any bugs - Thanks.

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Auto Tab Auto Clear
Pick an example here


Quick help: Using this Solver

Use the "Import" button or type in a Sudoku puzzle in the small board. You can also pick examples from the list above.
Click on Take Step to step through the solution. Unknown squares are filled with 'candidates' - possible solutions.
Any cells that are reduced to one possible candidate are solved.

You can now use the << button to step back one go. Toggling between Take Step and << helps you see the changes.

Pressing "Enter" on the keyboard after clicking on Take Step is a quick way to step through all strategies. Details of any solutions will be written out in the textbox below the big board. Strategies are ordered by complexity. Any that are successful returns the step-though to the start.

Click on the board to highlight sets of numbers. You can edit the sudoku at any time - entering solutions in the small board or editing candidates (Toggle between highlighting and editing using the radio buttons at the top.)

A
B
C
D
E
F
G
H
J
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
Version 1.99
See Strategy Overview documentation

Coordinate system: Letter/Number rYcX

 

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9


Welcome to my Sudoku page

Since I first studied Sudoku in May 2005 I think I've finally got a handle on this puzzle. My original intention was to prove to myself that a small number of simple strategies existed that could solve every sudoku. How wrong I was. Sudoku has enormous depth and while this solver has grown up enough to crack 99.9% of puzzles there are many weird and wonderful examples that defeat it. The main reason to keep this solver in development is to analyse these difficult ones. To that end I've added new graphical tools and features which I hope you'll enjoy.

Version 1.30 is a major update since I've found a way to include all the advanced strategies in my off-line C++ solver that were simply not possible to program in Javascript. Much still remains in javascript but its mostly user interface stuff now.

I am continuing to document the various strategies myself and many other people have invented. These are available here.

But in many cases progress has out stripped the documentation and I can only provide links to the best resources. I've tried to give credit where credit is due and please update me if I have missed anyone or need to make a correction.

I am now working independently on puzzle creation, especially at www.str8ts.com.

All feedback, comments, arguments, bug reports and strategy ideas are welcome. There is a FEEDBACK form with a column displaying comments and questions. Many thanks to all the people who have done so and helped improve this solver.



Original version 1.01 28th May 2005 - Full version history here

New in version 1.99 (April 9th 2014)
Unchecked strategies are now saved in a cookie.

New in version 1.98 (Sept 26th 2013)
Fixed Naked/Hidden Pairs/Triples to stop knock-on Pairs/Triples but allow multiple independent instances. See What's new for more info.

New in version 1.97 (July 22th 2013)
Added a tool to show strong links on the board. Under the strategy list.

New in version 1.96 (July 20th 2013)
Much expanded WXYZ-Wings detection. Separated and moved XYZ-Wings to tough strategies.

New in version 1.92 (March 20th 2013)
Solvers update (website and internal). Created the button for hull HTML output from a grade request showing all the steps of the puzzle.

New in version 1.93 (May 21th 2013)
Sudoku solver update (internal). Re-wrote the Forcing Chains strategies to improve detection (new cases) and the language of the result. Added 3D Medusa Rule 7.


Many people have written to me to comment about multiple solutions for a given Sudoku. There are no logical tricks the solver can use to detect this other than not complete correctly. The only way to check this is to perform a brute force analysis which tests every possible legal placement of a number. Computers are good at this and we now have a new yellow button called "Solution Count". Try this on any Sudoku to check if it has a unique solution.

Detailed help

Use Clear to empty the board before entering your own puzzle. Save will remember the current state of the board so you can Re-load it again (even if you close your browser - you must allow cookies for this to work). Restart applies only to the example puzzles in the list. The current list contains an example puzzle that tests each strategy.

Take Step first displays the possibles or candidates for each unknown cell. These are the numbers that do not contradict any known or solved square. Once these are displayed Take Step will step through other tests and then loop until it can go no further. The first few tests are the most productive and the solver will often loop between them. If any are successful and the board is changed in any way it will go back to the start and "Check for Solved Squares". The reason for this step is to make it easier to spot what's changed. Many of the strategies have knock-on effects which mean that they can't be run back-to-back - it's essential that we return to the basic steps. We go back because we want the easiest solve route.

> The first six tests are the simplest and are required for any sudoku. After that you are allowed to choose which strategies the solver will use. Tick and un-tick the check boxes.

> The order of these advanced strategies - and my inclusion of them in categories 'tough', 'diabolical' and 'extreme' are my personal choice after close study and are roughly in order of complexity. While the logic is different for each you should be aware that there is considerable overlap in their power to solve in certain situations. For example, X-Cycles are a subset of Alternating Inference Chains. If you turn off X-Cycles the same elimination might turn up under AICs. Since March 2010 I have re-worked most chaining strategies to find the best and shortest chains - not necessarily the first one it happens to find. More about what 'best' will be posted as a document.

> All strategies in the list have links to documentation, but its worth describing what the first tests do:

  • Show Possibles (Naked Singles): For each unknown square we eliminate all possibles where those numbers are known in each row, column and box. This may reveal a single candidate in which case we have a solution for that cell.
  • Hidden Singles: If a candidate occurs once in a row or column or box we can make it this the solution to the cell.
  • Test 2: In this test we check for 'naked' Pairs and Triples. For example, if we have two pairs, eg 3-4 and 3-4 in the same row, column or box, then both 3 and 4 must occupy those squares (in what ever order). 3 and 4 can then be eliminated from the rest of the row, column or box.
  • Test 3: This test is for Hidden Pairs, Hidden Triples
  • Test 4: Naked and Hidden Quads - much rarer but simply extends Pairs and Triples.
  • Test 5: See pointing pairs and triples for a full explanation. This test help us eliminate numbers in rows and columns outside the box.
  • Test 6: Box/Line Reduction. We check the box against the rows and columns that intersect it for each number.
If this solver comes up with an error - or it can't be solved, first use the Solution Count button to prove it has only one solution. This uses a fast brute-force algorithm to check for all possible solutions. If it's valid, please use the Email button to send it to andrew@scanraid.com. I'd be very interested to study examples that can't be solved on this page.



Solver created on 28-May-2005.

This page was last modified on 04-Feb-2014.
All code and design is copyright and for personal use only and may not be reproduced elsewhere.
Copyright Andrew Stuart @ Syndicated Puzzles Inc, 2005-2014