Welcome to my Sudoku X page
Sudoku X is a great variant of normal Sudoku and this solver is an extension of my Sudoku Solver to help
you discover the logical solutions for this puzzle. The difference is that in Sudoku X the two diagonals are known to contain
the numbers 1 ro 9 uniquely. These extra constraints allow you the puzzle solver to dervice new conclusions about candidates
to eliminate and find solutions to cells. You can look along the diagonals (marked with a darked X on th board) and make
deductions. However, the extra constraints mean that the puzzle creator can leave less clues than normal sudoku.
For the easier Sudoku X puzzles you won't really find a necessary example of a deduction based on the diagonals although
you will want to scan them in case you see an easy 'single'. For tough puzzles and above the diagonals must be checked. In this
solver they are checked before rows, columns and boxes. All the normal rules and logical posibilities apply to Sudoku X with
some exceptions. There are pitfalls, for example, with Unique Rectangles, which rely on a certain formations. I have documented
these here. Please check this stratgy guide if you want to use the advanced strategies.
I am now working independently on puzzle creation.
All feedback, comments, arguments, bug reports and strategy ideas are welcome. There is a new
FEEDBACK form with a column displaying comments and questions.
Many thanks to all the people who have done so and helped improve this solver.
Latest version 1.85 (May 12th 2011)
On the small board for number entry I have added an option that automatically clears off candidates as numbers are added.
Also, changes to the small board are automatically saved.
Latest version 1.82 (May 10th 2011)
I have redesigned the way cookies are stored and puzzles loaded. You still have a manual save and reload but
the solver now automatically saves the board every time it changes. Should you loose the page it will restore
the puzzle you were working on. Cookies also retain the difference between clues and solved cells as well.
Latest version 1.81 (April 20th 2012)
Restored Unique Rectangles to the Sudoku X solver. Added a special kind of Sudoku X Pointng Pair previously found by Simple Colouring. There have been a number of miner fixes to the solver in February and March not worthy of a version increment.
Version history here
Original version 1.42 12th Jan 2008
Notes on examples
The examples in the list above illustrate some of the many strategies available. They are
all 'necessary' examples in the sense that no easier strategy will by-pass the requirement for
their use - unless perhaps one reorders the strategies. The diabolical strategies could all be
swapped around to no detriment but I have ordered them in what I subjectively believe to be an
order of complexity. Some examples start at the beginning of the puzzles, some half way through.
While one strategy has been picked out as the example many of the others will be required to
Michael from Denmark has sent me the 'Unsolvable' - a great puzzle from a Sudoku magazine which I can't logically solve yet
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.
Use New 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 cookie for this to work).
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 least hard solve route.
The first seven 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. For example,
you may not want to use any strategies that rely on a unique solution. Uncheck test 15.
The order of these advanced strategies - and my inclusion of them in categories 'tough', 'diabolical'
and 'evil' 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, 'Guardians' will never solve anything while
'Multi-colouring' is switched on since they both attack similar configurations.
All strategies in the list have links to documentation, but its worth describing what the first tests do:
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 firstname.lastname@example.org. I'd be very interested to study
examples that can't be solved on this page.
- Show Possibles: 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.
- Test 1: If a possible number
occurs once in a row or column we can eliminate other candidates and make this the solution to the square.
- Test 2: If a possible number occurs once in a diagonal or box (3 by 3 cell)
we can eliminate other candidates and make this the solution to the square. Same test as Test 1 but for boxes.
- Test 3: 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 4: This test is for Hidden Pairs and
- Test 5: This test is for Naked Quads and
- Test 6: See pointing pairs and triples for
a full explanation. This test help us eliminate numbers in rows and columns outside the box.
- Test 7: Box/Line Reduction.
We check the box against the rows and columns that intersect it for each number.