The 'Unsolveable' SudokuThe "last resort" technique used to solve a sudoku that resists all
known logical techniques is known as bifurcation. This is simply a fancy word used by mathematicians
for "forking". In other words if no square can be resolved to a single number you pick a likely square
containing two candidates and follow the path that one of those numbers leads. If the chosen number
results in a sudoku anomaly then you know that the other number was the correct one, but there's a
50/50 chance that your first choice was correct.
However, it may be that there is a logical way to solve some of these puzzles that is not among the
known methods. This page is for the sudoku experts who strive to find such techniques. Extreme methods
such as swordfish may only help to solve one in a thousand sudoku puzzles, but every new technique is
a valuable tool to the sudoku solver.
The puzzles below are guaranteed to have a unique solution, but defy known logical solving methods.
The first eleven published in November 2005 were soon picked off. The second eleven caused quite a bit
of debate but they have all fallen to logical talent. The lessons have been learnt with this new set.
Credit will be given for an elegant logical solution with a solve route if you publish it on the
Eureka forum and it stands
up to scrutiny (Nishio, Bowman's and other 'Trial and Error' will not count).
You can also download the data file for numbers 23-33.
Have fun, and the best of luck.
New 'Unsolvables' - September 13th 2006
| 23. |
. . .|8 . 2|1 . .
. 6 .|. 4 .|. 5 .
1 . .|. . .|. 7 2
-----+-----+-----
. . 5|9 . 6|7 . .
. . .|. 8 .|. . .
. . 1|3 . 4|8 . .
-----+-----+-----
2 5 .|. . .|. . 1
. 1 .|. 3 .|. 9 .
. . 3|4 . 1|. . .
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Printable version
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| 24. |
6 . .|. 8 .|. . 5
. 4 .|. . 1|2 8 .
. 8 .|. . .|. 6 .
-----+-----+-----
. . 7|. . 2|3 . .
. . .|5 . 8|. . .
. . 1|7 . .|. . .
-----+-----+-----
. 6 .|. . .|. 4 .
. . 4|3 . .|. 2 .
3 . .|. 9 .|. . 6
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Printable version
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| 25. |
4 . .|. 1 .|. . 5
6 . .|2 . 7|. . 4
. . .|. . .|1 . .
-----+-----+-----
. 4 .|9 . .|. 6 .
. . 2|. 5 .|8 . .
. 9 .|. . 4|. . .
-----+-----+-----
. . 7|. . .|. . .
8 . .|5 . 1|. . 3
1 . .|. 6 .|. . 8
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Printable version
Mike Barker required Death Blossom to solve this. Thread here.
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| 26. |
. 2 6|. . .|9 . .
. . 5|. 6 .|4 . .
. . .|9 . 7|. . .
-----+-----+-----
9 . .|1 . .|. . 5
. 4 .|. . .|2 8 .
5 . .|. . 3|. . 4
-----+-----+-----
. . .|6 . 2|. . .
. . 9|. 5 .|7 . .
. . 1|. . .|8 5 .
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Printable version
Mike Barker used grouped nice loops, Kraken Cell exclusion and BUG+4X to solve it. Thread here.
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| 27. |
. . .|. . 1|. . .
4 . .|9 . 8|. . 5
. . 2|. . .|6 . 8
-----+-----+-----
. 3 .|. 5 .|. 7 1
. 8 .|. . .|. 6 .
. 7 .|. 9 .|. 8 .
-----+-----+-----
3 . 9|. . .|4 . .
6 . .|4 . 5|. . 7
. . .|2 . .|. . .
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Printable version
Mike Barker used more Kraken Cell exclusion solve it on this thread.
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| 28. |
. . 5|. . .|8 . .
. 7 .|3 . .|. 1 .
8 . .|1 . 5|. . 9
-----+-----+-----
6 . .|. . .|. 7 4
. . .|2 . 6|. . .
2 9 .|. . .|. . 8
-----+-----+-----
3 . .|. . 4|. . 1
. 1 .|. . 9|. 4 .
. . 6|. . .|3 . .
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Printable version
Mike Barker insists there is nothing special about this one. Thread here.
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| 29. |
. . .|. . 8|. 6 .
1 9 .|. . .|. 7 .
. . 5|. 2 .|4 . .
-----+-----+-----
9 3 .|. . .|. 4 .
. . .|2 . 7|. . .
. 6 .|. . .|. 8 9
-----+-----+-----
. . 3|. 7 .|8 . .
. 5 .|. . .|. 2 6
. 1 .|3 . .|. . .
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Printable version
Mike Barker used VWXYZ-wings and grouped nice loops to solve this. Thread here.
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| 30. |
. 5 .|. . .|. 6 .
. . 4|. 2 .|3 . .
9 . .|. 4 .|. . 5
-----+-----+-----
. 9 6|. . .|5 . .
. . .|4 . 8|. . .
. . 5|. . .|1 3 .
-----+-----+-----
7 . .|. 6 .|2 . 3
. . 2|. 1 .|9 . .
. 3 .|. . .|. 7 .
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Printable version
Mike Barker used ALS to crack it. Thread here.
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| 31. |
. . .|. 5 .|. . .
. 4 .|2 . 8|. 9 .
. . 7|. 6 .|4 . 2
-----+-----+-----
. 8 .|. . .|. 7 .
7 . 6|. . .|2 . 5
. 5 .|. . .|. 4 .
-----+-----+-----
3 . 8|. 2 .|1 . .
. 7 .|9 . 1|. . .
. . .|. 3 .|. . .
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Printable version
Mike Barker used grouped nice loops and a UVWXYZ-wing. Thread here.
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| 32. |
9 . .|. 1 .|. . 3
. . .|4 . 7|. . .
. . 1|. 5 .|6 . .
-----+-----+-----
. 2 3|. . .|4 9 .
5 . .|. . .|. . 8
. . 8|. . .|7 2 .
-----+-----+-----
. . 6|. 4 .|5 . .
. . .|1 . 8|. . .
4 . .|. 9 .|. . 1
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Printable version
Mike Barker used grouped nice loops again. Thread here.
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| 33. |
. 1 .|. . .|. 5 .
7 . 8|. . .|. . .
. . 2|6 . 8|3 . .
-----+-----+-----
9 . .|3 . 5|. . 7
. . .|. . .|. . .
8 . .|4 . 2|. . 6
-----+-----+-----
. . 9|7 . 1|2 . .
. . 3|. . .|4 . .
. 8 .|. . .|. 9 .
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Printable version
StrmCkr puts a strong case solving this using the Limitation Rule. Thread here.
Gurth also has some interesting ideas.
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'Unsolvables' from April 2006
12.
0 0 7 3 0 0 4 0 0 r.e.s. proposed a solution with a
0 0 0 0 4 0 0 9 0 uniqueness arguement here, April 16th 2006
0 5 0 0 0 0 0 6 0
0 0 0 0 0 7 6 0 0
5 0 0 0 3 0 0 0 1
0 0 3 9 0 8 0 0 0
0 2 0 0 0 0 0 7 0
0 1 0 0 8 0 0 0 0
0 0 4 6 0 9 2 0 0
13.
0 0 0 2 0 1 0 3 0 Gurth Bruins proposed a solution
3 0 0 0 5 0 0 0 8 on this thread, April 2006
0 0 0 0 4 0 0 0 5
0 0 0 0 0 8 0 7 0 Stephen Kurzhals has an interesting
0 0 4 0 3 0 1 0 0 route published here, April 2006
0 9 0 5 0 0 0 2 0
9 0 0 0 8 0 0 0 0
6 0 0 0 0 0 0 0 7
0 3 0 9 0 5 0 0 0
14.
0 4 0 0 0 0 0 2 0 David P Bird ran this solution up
9 0 0 0 0 0 1 0 3 the flag pole here, May 32st 2006
0 0 2 3 0 7 9 0 0
0 0 0 1 0 4 0 0 0
8 0 0 0 0 0 0 0 4
0 0 0 7 0 5 0 9 0
0 0 8 5 0 2 6 0 0
1 0 9 0 0 0 0 0 8
0 6 0 0 0 0 0 7 0
15.
8 0 0 0 0 0 0 0 6 Anne Morelot proposed a solution using an
0 0 0 0 0 0 1 5 0 ALS XY-Wing on this thread, May 4th 2006
0 0 6 9 0 0 2 0 0
3 0 0 0 1 0 0 0 4
0 0 9 0 6 0 7 0 0
2 0 0 0 7 0 0 0 3
0 0 3 0 0 1 4 0 0
0 4 5 0 0 0 0 8 0
6 0 0 0 0 0 0 0 9
16.
0 9 0 3 0 0 0 0 0
0 0 7 0 0 0 6 0 0
0 0 0 0 2 4 0 3 0
9 1 0 0 0 0 0 0 8
0 0 0 0 0 0 0 0 0
4 0 0 0 0 5 0 2 7
0 5 0 8 7 0 0 6 0
0 0 1 0 0 0 5 0 0
0 0 0 5 0 6 0 9 0
17.
0 0 0 0 8 0 0 0 1 Anne Morelot proposed a solution using several
0 0 6 1 0 7 9 2 0 ALS tricks thread, May 4th 2006
0 1 0 0 4 0 0 5 0
0 0 0 0 0 8 0 0 3
0 0 0 0 0 0 7 0 0
4 0 0 5 0 0 0 0 0
0 8 0 0 2 0 0 9 0
0 3 9 6 0 1 8 0 0
0 0 0 0 9 0 0 0 0
18.
0 6 0 0 3 2 0 4 0 David P Bird proposed a solution
8 0 0 5 0 0 0 0 1 using Graded Equivalence Marking here,
0 0 9 0 0 0 0 0 0 June 8th 2006
0 0 0 0 0 0 2 9 0
0 0 0 7 0 3 0 0 0
0 1 4 0 0 0 5 0 0
0 0 8 0 0 0 3 0 0
7 0 0 0 0 6 0 0 9
0 2 0 4 8 0 0 5 0
19.
2 0 0 0 0 0 0 6 0 Bill Richter solves this one using
0 0 9 3 0 4 0 0 0 XY/Colouring/ALS Or Chains here, June 16th 2006
0 0 4 0 5 0 8 0 0 Carcul has an alternative here.
4 0 0 0 0 0 0 0 6
0 9 0 1 0 7 0 2 0
7 0 0 0 0 0 0 0 1
0 0 5 0 0 0 6 0 0
0 0 0 2 0 3 5 0 0
0 1 0 0 0 0 0 3 7
20.
0 0 1 0 5 0 7 0 0 Gurth Bruins proposed a solution
3 0 0 0 0 0 0 0 9 on this thread, June 3rd, 2006
0 2 0 7 0 0 1 4 0
0 0 0 9 0 2 0 0 1
0 0 3 0 0 0 5 0 0
6 0 0 4 0 0 0 0 0
0 8 4 0 0 6 0 3 0
5 0 0 0 0 0 0 0 7
0 0 6 0 9 0 8 0 0
21.
0 0 0 5 4 6 0 0 7 Cavan Fang proposed a solution first
4 0 0 0 0 0 0 0 9 using colouring chains on this thread
0 0 0 0 0 0 3 0 0
0 0 6 3 0 0 5 0 0
0 3 0 0 0 0 0 2 0
0 0 5 0 0 2 1 0 0
0 0 7 0 0 0 0 0 0
8 0 0 0 1 0 0 0 3
3 0 0 2 9 8 0 0 0
22.
0 6 0 0 8 0 0 2 0 Anne Morelot proposed a solution with
0 0 0 3 7 2 0 0 0 multi-colouring here, April 18th 2006.
7 0 0 0 0 0 1 0 5
0 0 4 0 0 0 3 0 0
0 9 0 0 0 8 0 6 0
0 0 7 0 0 0 2 0 0
3 0 8 0 0 0 0 0 0
0 0 0 4 0 5 0 0 0
0 5 0 0 2 0 0 9 0
Unsolvables from November 2005
These were unsolvable when posted in in November 2005. Four are still not cracked using logic. Please use our Feedback Form if you can show a logical path for the remaining. You'll be credited on this page.
1.
1 0 0 9 0 7 0 0 3 Rod Hagglund has proposed a
0 8 0 0 0 0 0 7 0 solution here, January 17, 2006
0 0 9 0 0 0 6 0 0 Shortly followed by post from
0 0 7 2 0 9 4 0 0 Cavan Fang here, January 26, 2006
4 1 0 0 0 0 0 9 5
0 0 8 5 0 4 3 0 0
0 0 3 0 0 0 7 0 0
0 5 0 0 0 0 0 4 0
2 0 0 8 0 6 0 0 9
2.
0 0 0 3 0 2 0 0 0 Rod Hagglund has proposed a
0 5 0 7 9 8 0 3 0 solution here, January 13, 2006
0 0 7 0 0 0 8 0 0 and also by
0 0 8 6 0 7 3 0 0 Cavan Fang here, January 31, 2006
0 7 0 0 0 0 0 6 0
0 0 3 5 0 4 1 0 0
0 0 5 0 0 0 6 0 0
0 2 0 4 1 9 0 5 0
0 0 0 8 0 6 0 0 0
3.
0 0 0 8 0 0 0 0 6 Solvable with a Y-Wing
0 0 1 6 2 0 4 3 0
4 0 0 0 7 1 0 0 2
0 0 7 2 0 0 0 8 0
0 0 0 0 1 0 0 0 0
0 1 0 0 0 6 2 0 0
1 0 0 7 3 0 0 0 4
0 2 6 0 4 8 1 0 0
3 0 0 0 0 5 0 0 0
4.
3 0 5 0 0 4 0 7 0 Solvable with a Remote Pair Chain
0 7 0 0 0 0 0 0 1
0 4 0 9 0 0 0 3 0
4 0 0 0 5 1 0 0 6
0 9 0 0 0 0 0 4 0
2 0 0 8 4 0 0 0 7
0 2 0 0 0 7 0 6 0
8 0 0 0 0 0 0 9 0
0 6 0 4 0 0 2 0 8
5.
0 0 0 7 0 0 3 0 0 Solvable using
0 6 0 0 0 0 5 7 0 Aligned Pair exclusion
0 7 3 8 0 0 4 1 0
0 0 9 2 8 0 0 0 0
5 0 0 0 0 0 0 0 9
0 0 0 0 9 3 6 0 0
0 9 8 0 0 7 1 5 0
0 5 4 0 0 0 0 6 0
0 0 1 0 0 9 0 0 0
6.
0 0 0 6 0 0 0 0 4 Solvable with a Y-Wing Chain
0 3 0 0 9 0 0 2 0
0 6 0 8 0 0 7 0 0
0 0 5 0 6 0 0 0 1
6 7 0 3 0 1 0 5 8
9 0 0 0 5 0 4 0 0
0 0 6 0 0 3 0 9 0
0 1 0 0 8 0 0 6 0
2 0 0 0 0 6 0 0 0
7.
8 0 0 0 0 1 0 4 0 Rod Hagglund and Bill Richter have
2 0 6 0 9 0 0 1 0 a solution, January 21, 2006
0 0 9 0 0 6 0 8 0 and also by
1 2 4 0 0 0 0 0 9 Cavan Fang here, March 31, 2006
0 0 0 0 0 0 0 0 0
9 0 0 0 0 0 8 2 4
0 5 0 4 0 0 1 0 0
0 8 0 0 7 0 2 0 5
0 9 0 5 0 0 0 0 7
8.
6 5 2 0 4 8 0 0 7 Solvable with a XY Chain
0 7 0 2 0 5 4 0 0
0 0 0 0 0 0 0 0 0
0 6 4 1 0 0 0 7 0
0 0 0 0 8 0 0 0 0
0 8 0 0 0 4 5 6 0
0 0 0 0 0 0 0 0 0
0 0 8 6 0 7 0 2 0
2 0 0 8 9 0 7 5 1
9.
0 0 6 0 0 2 0 0 9 Solvable using
1 0 0 5 0 0 0 2 0 Aligned Pair Exclusion
0 4 7 3 0 6 0 0 1 and XY-Chain
0 0 0 0 0 8 0 4 0
0 3 0 0 0 0 0 7 0
0 1 0 6 0 0 0 0 0
4 0 0 8 0 3 2 1 0
0 6 0 0 0 1 0 0 4
3 0 0 4 0 0 9 0 0
10.
0 0 4 0 5 0 9 0 0 Solvable with a XY Chain
0 0 0 0 7 0 0 0 6
3 7 0 0 0 0 0 0 2
0 0 9 5 0 0 0 8 0
0 0 1 2 0 4 3 0 0
0 6 0 0 0 9 2 0 0
2 0 0 0 0 0 0 9 3
1 0 0 0 4 0 0 0 0
0 0 6 0 2 0 7 0 0
11.
0 0 0 0 3 0 7 9 0 Bill Richter proposed a
3 0 0 0 0 0 0 0 5 solution, April 15, 2006
0 0 0 4 0 7 3 0 6
0 5 3 0 9 4 0 7 0
0 0 0 0 7 0 0 0 0
0 1 0 8 2 0 6 4 0
7 0 1 9 0 8 0 0 0
8 0 0 0 0 0 0 0 1
0 9 4 0 1 0 0 0 0
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