Mirrored from Sudopedia, the Free Sudoku Reference Guide

# Invalid Test Cases

Testing a good Sudoku solver should exercise the error handling as well as the algorithm. These test cases can be divided into to basic categories: puzzles that cannot be parsed, and puzzles that cannot be solved. A puzzle cannot be parsed if it violates any of the basic rules of Sudoku, or contains less than 17 given (starting) values. Alternately, many puzzles can be parsed successfully, but still cannot be solved: either the starting givens donâ€™t yield a single unique solution, or there is no possible solution.

## Empty

The ultimate in ‘not enough input’, this puzzle contains no givens at all. To say that it has multiple solutions is something of an overstatement.

Givens

```. . . | . . . | . . .
. . . | . . . | . . .
. . . | . . . | . . .
------+-------+------
. . . | . . . | . . .
. . . | . . . | . . .
. . . | . . . | . . .
------+-------+------
. . . | . . . | . . .
. . . | . . . | . . .
. . . | . . . | . . .
```
```.................................................................................
```

Solution

(multiple solutions)

Pass Condition

Invalid Puzzle (“not enough givens” / “multiple solutions”)

## Single Given

Originally described as ‘Zen Sudoku’, rumor has it that the only way to solve this puzzle is to stare at the lone ‘1’ in the center of the grid. Expected results could include “not enough starting values” or “multiple solutions”.

Givens

```. . . | . . . | . . .
. . . | . . . | . . .
. . . | . . . | . . .
------+-------+------
. . . | . . . | . . .
. . . | . 1 . | . . .
. . . | . . . | . . .
------+-------+------
. . . | . . . | . . .
. . . | . . . | . . .
. . . | . . . | . . .
```
```........................................1........................................
```

Solution

(500+ solutions)

Pass Condition

Invalid Puzzle (“not enough givens” / “multiple solutions”)

## Insufficient Givens

This puzzle has only sixteen givens, which is one less than the accepted minimum number for a classic Sudoku puzzle. Expected results could include “not enough starting values” or “multiple solutions”.

Givens

```. . . | . . . | . . .
. . 5 | . . . | . 9 .
. . 4 | . . . | . 1 .
------+-------+------
2 . . | . . 3 | . 5 .
. . . | 7 . . | . . .
4 3 8 | . . . | 2 . .
------+-------+------
. . . | . 9 . | . . .
. 1 . | 4 . . | . 6 .
. . . | . . . | . . .
```
```...........5....9...4....1.2....3.5....7.....438...2......9.....1.4...6..........
```

Solution

(500+ solutions)

Pass Condition

Invalid Puzzle (“not enough givens” / “multiple solutions”)

## Duplicate Given — Box

This puzzle cannot be solved, because the middle box (b5) has the value ‘5’ twice.

Givens

```. . 9 | . 7 . | . . 5
. . 2 | 1 . . | 9 . .
1 . . | . 2 8 | . . .
------+-------+------
. 7 . | . . 5 | . . 1
. . 8 | 5 1 . | . . .
. 5 . | . . . | 3 . .
------+-------+------
. . . | . . 3 | . . 6
8 . . | . . . | . . .
2 1 . | . . . | . 8 7
```
```..9.7...5..21..9..1...28....7...5..1..851.....5....3.......3..68........21.....87
```

Solution

(no solution)

Pass Condition

Invalid Puzzle (“no solution”)

## Duplicate Given — Column

This puzzle cannot be solved, because the middle column (c5) has the value ‘1’ twice.

Givens

```6 . 1 | 5 9 . | . . .
. 9 . | . 1 . | . . .
. . . | . . . | . . 4
------+-------+------
. 7 . | 3 1 4 | . . 6
. 2 4 | . . . | . . 5
. . 3 | . . . | . 1 .
------+-------+------
. . 6 | . . . | . . 3
. . . | 9 . 2 | . 4 .
. . . | . . 1 | 6 . .
```
```6.159.....9..1............4.7.314..6.24.....5..3....1...6.....3...9.2.4......16..
```

Solution

(no solution)

Pass Condition

Invalid Puzzle (“no solution”)

## Duplicate Given — Row

This puzzle cannot be solved, because the middle row (r5) has the value ‘2’ twice.

Givens

```. 4 . | 1 . . | 3 5 .
. . . | . . . | . . .
. . . | 2 . 5 | . . .
------+-------+------
. . . | 4 . 8 | 9 . .
2 6 . | . . . | . 1 2
. 5 . | 3 . . | . . 7
------+-------+------
. . 4 | . . . | 1 6 .
6 . . | . . 7 | . . .
. 1 . | . 8 . | . 2 .
```
```.4.1..35.............2.5......4.89..26.....12.5.3....7..4...16.6....7....1..8..2.
```

Solution

(no solution)

Pass Condition

Invalid Puzzle (“no solution”)

## Unsolvable Square

This puzzle cannot be solved, because the left-most square of the middle row (r5c1) has no possible candidates.

Givens

```. . 9 | . 2 8 | 7 . .
8 . 6 | . . 4 | . . 5
. . 3 | . . . | . . 4
------+-------+------
6 . . | . . . | . . .
. 2 . | 7 1 3 | 4 5 .
. . . | . . . | . . 2
------+-------+------
3 . . | . . . | 5 . .
9 . . | 4 . . | 8 . 7
. . 1 | 2 5 . | 3 . .
```
```..9.287..8.6..4..5..3.....46.........2.71345.........23.....5..9..4..8.7..125.3..
```

Solution

(no solution)

Pass Condition

Invalid Puzzle (“no solution”)

## Unsolvable Box

This puzzle cannot be solved, because the center box (b5) has no possible candidates for the value ‘4’.

Givens

```. 9 . | 3 . . | . . 1
. . . | . 8 . | . 4 6
. . . | . . . | 8 . .
------+-------+------
4 . 5 | . 6 . | . 3 .
. . 3 | 2 7 5 | 6 . .
. 6 . | . 1 . | 9 . 4
------+-------+------
. . 1 | . . . | . . .
5 8 . | . 2 . | . . .
2 . . | . . 7 | . 6 .
```
```.9.3....1....8..46......8..4.5.6..3...32756...6..1.9.4..1......58..2....2....7.6.
```

Solution

(no solution)

Pass Condition

Invalid Puzzle (“no solution”)

## Unsolvable Column

This puzzle cannot be solved, because the middle column (c5) has no possible candidates for the value ‘2’.

Givens

```. . . | . 4 1 | . . .
. 6 . | . . . | . 2 .
. . 2 | . . . | . . .
------+-------+------
3 2 . | 6 . . | . . .
. . . | . 5 . | . 4 1
7 . . | . . . | . . 2
------+-------+------
. . . | . . . | 2 3 .
. 4 8 | . . . | . . .
5 . 1 | . . 2 | . . .
```
```....41....6.....2...2......32.6.........5..417.......2......23..48......5.1..2...
```

Solution

(no solution)

Pass Condition

Invalid Puzzle (“no solution”)

## Unsolvable Row

This puzzle cannot be solved, because the middle row (r5) has no possible candidates for the value ‘1’.

Givens

```9 . . | 1 . . | . . 4
. 1 4 | . 3 . | 8 . .
. . 3 | . . . | . 9 .
------+-------+------
. . . | 7 . 8 | . . 1
8 . . | . . 3 | . . .
. . . | . . . | . 3 .
------+-------+------
. 2 1 | . . . | . 7 .
. . 9 | . 4 . | 5 . .
5 . . | . 1 6 | . . 3
```
```9..1....4.14.3.8....3....9....7.8..18....3..........3..21....7...9.4.5..5...16..3
```

Solution

(no solution)

Pass Condition

Invalid Puzzle (“no solution”)

## Not Unique — 2 Solutions

This puzzle is not a valid Sudoku, because it has two possible solutions.

Givens

```. 3 9 | . . . | 1 2 .
. . . | 9 . 7 | . . .
8 . . | 4 . 1 | . . 6
------+-------+------
. 4 2 | . . . | 7 9 .
. . . | . . . | . . .
. 9 1 | . . . | 5 4 .
------+-------+------
5 . . | 1 . 9 | . . 3
. . . | 8 . 5 | . . .
. 1 4 | . . . | 8 7 .
```
```.39...12....9.7...8..4.1..6.42...79...........91...54.5..1.9..3...8.5....14...87.
```

Solution

```439658127156927384827431956342516798785294631691783542578149263263875419914362875
439658127156927384827431956642513798785294631391786542578149263263875419914362875
```

Pass Condition

Invalid Puzzle (“no unique solution”)

## Not Unique — 3 Solutions

This puzzle is not a valid Sudoku, because it has three possible solutions.

Givens

```. . 3 | . . . | . . 6
. . . | 9 8 . | . 2 .
9 4 2 | 6 . . | 7 . .
------+-------+------
4 5 . | . . 6 | . . .
. . . | . . . | . . .
1 . 9 | . 5 . | 4 7 .
------+-------+------
. . . | . 2 5 | . 4 .
6 . . | . 7 8 | 5 . .
. . . | . . . | . . .
```
```..3.....6...98..2.9426..7..45...6............1.9.5.47.....25.4.6...785...........
```

Solution

```783542196516987324942631758457296813238714965169853472891325647624178539375469281
783542916516987324942631758457216839238794165169853472891325647624178593375469281
783542916516987324942631758457216893238794165169853472891325647624178539375469281
```

Pass Condition

Invalid Puzzle (“no unique solution”)

## Not Unique — 4 Solutions

This puzzle is not a valid Sudoku, because it has four possible solutions.

Givens

```. . . | . 9 . | . . .
6 . . | 4 . 7 | . . 8
. 4 . | 8 1 2 | . 3 .
------+-------+------
7 . . | . . . | . . 5
. . 4 | . . . | 9 . .
5 . . | 3 7 1 | . . 4
------+-------+------
. 5 . | . 6 . | . 4 .
2 . 1 | 7 . 8 | 5 . 9
. . . | . . . | . . .
```
```....9....6..4.7..8.4.812.3.7.......5..4...9..5..371..4.5..6..4.2.17.85.9.........
```

Solution

```178693452623457198945812736716984325384526917592371684857169243231748569469235871
178693452623457198945812736716984325384526971592371684857169243231748569469235817
178693452623457198945812736762984315314526987589371624857169243231748569496235871
178693452623457198945812736786924315314586927592371684857169243231748569469235871
```

Pass Condition Invalid Puzzle (“no unique solution”)

## Not Unique — 10 Solutions

This puzzle is not a valid Sudoku, because it has ten possible solutions.

Givens

```5 9 . | . . . | . 4 8
6 . 8 | . . . | 3 . 7
. . . | 2 . 1 | . . .
------+-------+------
. . . | . 4 . | . . .
. 7 5 | 3 . 6 | 9 8 .
. . . | . 9 . | . . .
------+-------+------
. . . | 8 . 3 | . . .
2 . 6 | . . . | 7 . 9
3 4 . | . . . | . 6 5
```
```59.....486.8...3.7...2.1.......4.....753.698.....9.......8.3...2.6...7.934.....65
```

Solution

```592637148618459327437281596923748651175326984864195273759863412286514739341972865
592637148618459327437281596963748251175326984824195673759863412286514739341972865
592637148618459327734281596129748653475326981863195274957863412286514739341972865
592637148618459327734281596129748653475326981863195472957863214286514739341972865
592637148618459327734281596169748253475326981823195674957863412286514739341972865
592637148618459327734281596829145673175326984463798251957863412286514739341972865
592637148618459327734281596829145673475326981163798254957863412286514739341972865
592637148618459327734281596829145673475326981163798452957863214286514739341972865
592637148618459327734281596869145273175326984423798651957863412286514739341972865
592637148618459327734281596869145273475326981123798654957863412286514739341972865
```

Pass Condition

Invalid Puzzle (“no unique solution”)

## Not Unique — 125 Solutions

This puzzle is not a valid Sudoku, because it has 125 possible solutions.

Givens

```. . . | 3 1 6 | 5 . .
8 . . | 5 . . | 1 . .
. 1 . | 8 9 7 | 2 4 .
------+-------+------
9 . 1 | . 8 5 | . 2 .
. . . | 9 . 1 | . . .
. 4 . | 2 6 3 | . . 1
------+-------+------
. 5 . | . . . | . 1 .
1 . . | 4 . 9 | . . 2
. . 6 | 1 . 8 | . . .
```
```...3165..8..5..1...1.89724.9.1.85.2....9.1....4.263..1.5.....1.1..4.9..2..61.8...
```

Solution

```274316589893524167615897243931785426562941378748263951359672814187459632426138795
274316589893524167615897243931785426762941358548263791359672814187459632426138975
274316589893524167615897243931785426762941358548263971359672814187459632426138795
274316589893524167615897243931785426762941835548263791459672318187439652326158974
274316589893524167615897243931785426762941835548263971459672318187439652326158794
```

```724316598869524173315897246931785624682941357547263981458632719173459862296178435
724316598869524173315897246931785624682941735547263981453672819178459362296138457
724316598869524173315897246931785624682941735547263981458672319173459862296138457
724316598893524176615897243961785324382941765547263981459632817138479652276158439
724316598893524176615897243961785324382941765547263981459632817178459632236178459
```

Pass Condition

Invalid Puzzle (“no unique solution”)