Sudoku Solve App

LOADING AND EDITING SUDOKU

Loading and Entering Sudoku Clues:

1) Load As Image: File > Open > As Image
Take photo or screen capture. Ideally trimmed to just outside the main Sudoku square.
Image will be AI processed to extract digits. Choose Ok to accept result.
File format is *.jpg or *.bmp.

2) Load as text: File > Open > As Text
Text format is number string with 0 for empty Cells, i.e.
809630700000000800450000010000100073000825901190000028030000096007000080000014207
or comma separated.
File format is *.txt.

3) Load by Paste: File > Open > Paste Text
First copy a Sudoku from text to clipboard. Paste format is number string with 0 for empty Cells, i.e.
809630700000000800450000010000100073000825901190000028030000096007000080000014207
or comma separated.

4) Number Entry: Select a Cell: Selected Cell is coloured Blue.
a) Enter numbers with keyboard or
b) Select button "Clue #" and use number-pad above Sudoku or
c) Right click Cell. Enter number from menu or
d) Use Menu Dropdown > Edit > Clue # > Select number or
e) Delete numbers with keyboard. Highlight text then delete or backspace.

Entering Solve numbers:

1) Solve Number Entry: Select a Cell: Selected Cell is coloured Blue.
a) Enter numbers with keyboard or
b) Select button "Solve #" and use number-pad above Sudoku or
c) Right click Cell. Enter number from menu or
d) Use Menu Dropdown > Edit > Solve # > Select number or
e) Remove entry and go back a step with back button "<".

Editing Candidates:

1) Candidate Edit: Select a Cell: Selected Cell is coloured Blue.
a) Highlight a Candidate in Cell then delete or backspace with keyboard or
b) Select button "Candidate(Auto)" and use number-pad above Sudoku or
c) Right click Cell. Enter number from menu or
d) Use Menu Dropdown > Edit > Candidate(Auto) > Select number or
e) Undo change and go back a step with back button "<".

ALGORITHMS

Algorithm: Candidates Row,Column,Block
The Candidates (in blue) are the options of possible Solution numbers. They are cleared automatically if the same number is in the same Row, Column or Block. To hide the auto generated Candidate display, or to enter Candidates manually, you can disable menu:[View > Auto Candidate].

e.g. In Cell R1C2 [Row=1,Col=2], Row #4#6#5#1#2, Col #3#6#8#4 and Block #3 clear all Candidates except #7 and #9.

Algorithm: Single In Cell
The Candidate is the only option in a Cell.

e.g. #9 in Cell R1C2 [Row=1,Col=2] is the only Candidate in the Cell. Set Cell R1C2 to #9.

Algorithm: Single In Row
The Candidate is in only one Cell in a Row.

e.g. #7 in Row 2 is only in Cell R2C6 [Row=2,Col=6]. Set Cell R2C6 to #7.

Algorithm: Single In Column
The Candidate is in only one Cell in a Column.

e.g. #7 in Col 2 is only in Cell R3C2 [Row=3,Col=2]. Set Cell R3C2 to #7.

Algorithm: Single In Block
The Candidate is in only one Cell in a Block.

e.g. #7 in Block 1 is only in Cell R3C2 [Row=3,Col=2]. Set Cell R3C2 to #7.

Algorithm: Line Block -Clear Line
If a Candidate number within a Block can only be in one Line (Row or Column), then the Candidate can be cleared elsewhere on the Line.

e.g. #5 in Block 1 can only be in Column 1, R2C1 or R3C1. It can therefore be cleared elsewhere on Column 1. Can clear Candidate #5 from Cell R7C1.

Algorithm: Line Block -Clear Block
If a Candidate number in a Line can only be in one Block, then the Candidate can be cleared elsewhere in the Block.

e.g. #5 in Column 2 can only be in Block 7, R7C2 or R8C2. It can therefore be cleared elsewhere in Block 7. Can clear Candidate #5 from Cell R7C1.

Algorithm: Pairs In Row
If two Cells in a Row contain the same and only two Candidates. Then the Candidate numbers can be cleared from other Cells in the Row.

e.g. Candidates #2#4 are alone in Cells R1C3 and R1C4. So Solution numbers #2 and #4 must be in Cells R1C3 and R1C4, either way round. Therefore, can clear Candidates #2#4 from other cells in the Row i.e. #4 from R1C2 and R1C9.

Algorithm: Pairs In Column
If two Cells in a Column contain the same and only two Candidates. Then the Candidate numbers can be cleared from other Cells in the Column.

e.g. Candidates #2#4 are alone in Cells R2C9 and R8C9. So Solution numbers #2 and #4 must be in Cells R2C9 and R8C9, either way round. Therefore, can clear Candidates #2#4 from other cells in the Column i.e. #2#4 from R6C9 and R9C9.

Algorithm: Pairs In Block
If two Cells in a Block contain the same and only two Candidates. Then the Candidate numbers can be cleared from other Cells in the Block.

e.g. Candidates #2#4 are alone in Cells R1C8 and R2C9. So Solution numbers #2 and #4 must be in Cells R1C8 and R2C9, either way round. Therefore, can clear Candidates #2#4 from other cells in the Block i.e. #2#4 from R1C7 and R2C7.

Algorithm: Pairs Hidden In Row
If only two Cells in a Row have the same two Candidates, but with other Candidates in the two Cells. Then the other Candidates can be cleared from the two Cells.

e.g. Candidates #6#8 are only in Cells R1C2 and R1C9 in Row 1. So Solution numbers #6 and #8 must be in Cells R1C2 and R1C9, either way round. Therefore, can clear other Candidates from the two Cells, i.e. #4, from Cells R1C2 and R1C9.

Algorithm: Pairs Hidden In Col
If only two Cells in a Col have the same two Candidates, but with other Candidates in the two Cells. Then the other Candidates can be cleared from the two Cells.

e.g. Candidates #1#6 are only in Cells R1C7 and R2C7 in Column 7. So Solution numbers #1 and #6 must be in Cells R1C7 and R2C7, either way round. Therefore, can clear other Candidates from the two Cells, i.e. #2#4, from Cells R1C7 and R2C7.

Algorithm: Pairs Hidden In Block
If only two Cells in a Block have the same two Candidates, but with other Candidates in the two Cells. Then the other Candidates can be cleared from the two Cells.

e.g. Candidates #1#6 are only in Cells R1C7 and R2C7 in Block 3. So Solution numbers #1 and #6 must be in Cells R1C7 and R2C7, either way round. Therefore, can clear other Candidates from the two Cells, i.e. #2#4, from Cells R1C7 and R2C7.

Algorithm: Triples In Row
If three Candidate numbers only appear in three Cells in a Row and there are no other Candidate numbers in the three Cells. Note, all three Candidates don't need to be in each of the three Cells.Then the three Candidate numbers can be cleared from other Cells in the Row.

e.g. Candidates #1#3#8 are alone in Cells R2C3, R2C6 and R2C8 in Row 2. So Solution numbers #1, #3 and #8 must be in Cells R2C3, R2C6 and R2C8, in unknown order. Therefore, can clear Candidates #1#3#8 from other cells in the Row i.e. #1#8 from R2C7 and #1 from R2C9.

Algorithm: Triples In Column
If three Candidate numbers only appear in three Cells in a Column and there are no other Candidate numbers in the three Cells. Note, all three Candidates don't need to be in each of the three Cells.Then the three Candidate numbers can be cleared from other Cells in the Column.

e.g. Candidates #1#3#8 are alone in Cells R2C2, R4C2 and R7C2 in Column 2. So Solution numbers #1, #3 and #8 must be in Cells R2C2, R4C2 and R7C2, in unknown order. Therefore, can clear Candidates #1#3#8 from other cells in the Column i.e. #1 from R1C2 and #1#8 from R3C2.

Algorithm: Triples In Block
If three Candidate numbers only appear in three Cells in a Block and there are no other Candidate numbers in the three Cells. Note, all three Candidates don't need to be in each of the three Cells.Then the three Candidate numbers can be cleared from other Cells in the Block.

e.g. Candidates #1#5#8 are alone in Cells R2C1, R2C3 and R3C1 in Block 1. So Solution numbers #1, #5 and #8 must be in Cells R2C1, R2C3 and R3C1, in unknown order. Therefore, can clear Candidates #1#5#8 from other cells in the Block i.e. #1#5 from R3C2 and #1#8 from R3C3.

Algorithm: Triples Hidden In Row
If only three Cells in a Row have the same three Candidates, but with other Candidates in the three Cells. Then the other Candidates can be cleared from the three Cells.

e.g. Candidates #4#5#9 are only in Cells R2C5, R2C7 and R2C9 in Row 2. So Solution numbers #4, #5 and #9 must be in Cells R2C5, R2C7 and R2C9, in unknown order. Therefore, can clear other Candidates from the three Cells, i.e. #1#8 from Cell R2C7 and #1 from R2C9.

Algorithm: Triples Hidden In Column
If only three Cells in a Column have the same three Candidates, but with other Candidates in the three Cells. Then the other Candidates can be cleared from the three Cells.

e.g. Candidates #4#5#9 are only in Cells R1C2, R3C2 and R5C2 in Column 2. So Solution numbers #4, #5 and #9 must be in Cells R1C2, R3C2 and R5C2, in unknown order. Therefore, can clear other Candidates from the three Cells, i.e. #1 from Cell R1C2 and #1#8 from R3C2.

Algorithm: Triples Hidden In Block
If only three Cells in a Block have the same three Candidates, but with other Candidates in the three Cells. Then the other Candidates can be cleared from the three Cells.

e.g. Candidates #2#7#9 are only in Cells R1C2, R3C2 and R3C3 in Block 1. So Solution numbers #2, #7 and #9 must be in Cells R1C2, R3C2 and R3C3, in unknown order. Therefore, can clear other Candidates from the three Cells, i.e. #1#5 from Cell R3C2 and #1#8 from R3C3.

Algorithm: X-Wings -Rows, Clear Columns (2 lines)
For a Candidate number, two Rows have the Candidate only in the same two Column positions. From Row perspective, the Solution number has to be in either of the Row Cells, it follows from Column perspective the Solution number has to be in either of the two Column Cells. As the Candidate can only be in these two possible Column Cells it can be cleared in other Cells in the Column.

e.g. Candidate #6 in Row 4 and Row 9 is only in the Columns 3 and 9. The Candidate #6 can be cleared from other Column 3 and 9 Cells. i.e. Clear #6 from Cells R1C9 and R7C9.Note: The Solution #6 can only be in Cells R4C3+R9C9 or R4C9+R9C3. Hence the "X" in X-Wings.

Algorithm: X-Wings -Columns, Clear Rows (2 lines)
For a Candidate number, two Columns have the Candidate only in the same two Row positions. From Column perspective, the Solution number has to be in either of the Column Cells, it follows from Row perspective the Solution number has to be in either of the two Row Cells. As the Candidate can only be in these two possible Row Cells it can be cleared in other Cells in the Row.

e.g. Candidate #6 in Column 1 and Column 7 is only in the Rows 6 and 7. The Candidate #6 can be cleared from other Row 6 and 7 Cells. i.e. Clear #6 from Cells R7C8 and R7C9.

Algorithm: SwordFish -Rows, Clear Columns (3 lines)
Similar to X-Wings-Rows, except over three lines. For a Candidate number, three Rows have the Candidate only in Cells of the same three Columns. From the Row perspective, the Solution number has to be in only one of the Row's Cells, it follows from the Column perspective the Solution number has to be in only one of the Column's Cells. As the Candidate has to be in one of these possible Column Cells it can be cleared in other Cells in the Column.

e.g. Candidate #4 for each Row 2,8,9 is in some of the Columns 2,5,9. The Candidate #4 can be cleared from other Column 2,5,9 Cells. i.e. Clear #4 from Cells R3C5 and R7C2.Note: The Solution #4 can only be in Cells R2C2+R8C5+R9C9 or R2C5+R8C9+R9C2. Hence clear Candidate #4 from other Cells in these Columns.

Algorithm: SwordFish -Columns, Clear Rows (3 lines)
Similar to X-Wings-Columns, except over three lines. For a Candidate number, three Columns have the Candidate only in Cells of the same three Rows. From the Column perspective, the Solution number has to be in only one of the Column's Cells, it follows from the Row perspective the Solution number has to be in only one of the Row's Cells. As the Candidate has to be in one of these possible Row Cells it can be cleared in other Cells in the Row.

e.g. Candidate #4 for each Column 2,8,9 is in some of the Rows 1,5,8. The Candidate #4 can be cleared from other Row 1,5,8 Cells. i.e. Clear #4 from Cells R5C3 and R8C7.

Algorithm: JellyFish -Rows, Clear Columns (4 lines)
Similar to X-Wings and SwordFish, except over four lines. For a Candidate number, four Rows have the Candidate only in Cells of the same four Columns. From the Row perspective, the Solution number has to be in only one of the Row's Cells, it follows from the Column perspective the Solution number has to be in only one of the Column's Cells. As the Candidate has to be in one of these possible Column Cells it can be cleared in other Cells in the Column.

e.g. Candidate #4 for each Row 2,4,6,8 is in some of the Columns 1,5,7,9. The Candidate #4 can be cleared from other Column 1,5,7,9 Cells. i.e. Clear #4 from Cells R1C5, R5C7, R9C5 and R9C7.

Algorithm: JellyFish -Columns, Clear Rows (4 lines)
Similar to X-Wings and SwordFish, except over four lines. For a Candidate number, four Columns have the Candidate only in Cells of the same four Rows. From the Column perspective, the Solution number has to be in only one of the Column's Cells, it follows from the Row perspective the Solution number has to be in only one of the Row's Cells. As the Candidate has to be in one of these possible Row Cells it can be cleared in other Cells in the Row.

e.g. Candidate #4 for each Column 2,4,6,8 is in some of the Rows 1,5,7,9. The Candidate #4 can be cleared from other Row 1,5,7,9 Cells. i.e. Clear #4 from Cells R1C5, R5C7, R9C5 and R9C7.

Algorithm: Colour Chain Conflict
For a Candidate number, find pairs alone in a Row, Column or Block, and join the pairs to form a chain of pairs. Continue until back at the first Row, Column or Block. As a number is allowed only once per Row, Column or Block, the alternate numbers in chain must be true or false. The first and last in chain are false.

e.g. Candidate #6 has a pair chain (A-B, alternate red, green). Begins A1 and ends A5 which are both on Row 5. Clear Candidate #6 from A1,A3,A5. Set Solution #6 on B2,B4.

Algorithm: Colour Chain Eliminate
For a Candidate number, find pairs alone in a Row, Column or Block, and join the pairs to form a chain of pairs. The ends of the chain have a common Cell in the chain's ends Row, Column or Block containing the Candidate number. As the Chain ends are odd, i.e. if one true, the other is false, the Candidate number can be cleared from the common Cell.

e.g. Candidate #2 has a pair chain (A-B, alternate green, brown). Chain begins at A1 in Row 1 and ends at B4 in Column 1. As Row 1 and Column 1 meet at Cell R1C1, Candidate #2 can be cleared from Cell R1C1.

Algorithm: Colour Chains Multi
For a Candidate number, find pairs alone in a Row, Column or Block, and join pairs to form two chains of pairs. The two chains begin in a same Row, Column or Block and end in a same Row, Column or Block. The ends of the two chains can't form one chain due to the Candidate number being in another Cell in the Row, Column or Block. However, the chains are weakly linked as both Cells from each chain's ends can't be true at the same time. If by setting the chain ends true or false and following through the chains it can be shown the chains are strongly linked if the chain end match the appropriate true or false state. Then the Candidate number can be clear from other Cells in the chains end's Row, Column or Block.

e.g. For Candidate #4 there is Chain A and Chain B.
Chain A1 and Chain B1 are both in Row 5 (Both odd/green)
Chain A4 and Chain B4 are both in Block 9 (Both even/brown)
So can clear Candidate #4 from other cells in Row 5 and Block 9, i.e R5C3 and R8C7.

Algorithm: Trial Nishio -Candidate
This algorithm takes a Cell containing Candidate options, ideally with just two options, and tries selecting one of the options as the Solution number. Then try to solve the Sudoku as usual. If a conflict in numbers arises and it is evident the Sudoku is no longer solvable, then the selected Trial Candidate can be removed as a Candidate.

e.g. Candidate #2 is tried as the Solution number in Cell R1C3. The Sudoku is then not solvable, so the Candidate is not the valid Solution number. Therefore Candidate #2 can be removed as an option from Cell R1C3.

Algorithm: Trial Nishio -Solve
This algorithm takes a Cell containing Candidate options, ideally with just two options, and tries selecting one of the options as the Solution number. Then try to solve the Sudoku as usual. If a no conflict in numbers arises and the Sudoku is still solvable, then the selected Trial Candidate can be used as the valid Solution number.

e.g. Candidate #2 is tried as the Solution number in Cell R1C3. The Sudoku is still solvable, so the Candidate is the valid Solution number. Therefore Candidate #2 can be used as the Solution number for Cell R1C3.

Algorithm: Trial and Error
This algorithm is to test a Solution number in a first Cell, if the test attempt doesn't fail, then try a Solution number in a second Cell etc. Keep progressing if the Cell doesn't fail. If the Cell does fail, reject that test and try a different number or Cell to test. In this way a series of Cells with valid Solution numbers is found that solves the Sudoku.

e.g. T1 to T8 shows a successful Trial. Solution #4 was tried in Cell R2C3. As successful, Solution #5 was then tried in Cell R2C1 etc, until eighth Solution #4 in Cell R4C1 allowed the Sudoku to be solved. Set Solution numbers #4,5,1,6,4,6,7,4 in Cells R2C3,R2C1,R2C4,R2C7,R1C7,R1C2,R3C1,R4C1.