Rooted: Created page with "These test cases should result in a valid puzzle, and potentially a unique solution. == Completed Puzzle == A case of ‘more than enough’, this puzzle has already..."

2025-07-22T19:36:32Z

Created page with "These test cases should result in a valid puzzle, and potentially a unique solution. == Completed Puzzle == A case of ‘more than enough’, this puzzle has already..."

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These test cases should result in a valid puzzle, and potentially a unique solution.

== Completed Puzzle ==

A case of ‘more than enough’, this puzzle has already been solved. Nonetheless, it is still a valid puzzle, and should be parsed successfully.

'''Givens'''

9 7 4 | 2 3 6 | 1 5 8
6 3 8 | 5 9 1 | 7 4 2
1 2 5 | 4 8 7 | 9 3 6
------+-------+------
3 1 6 | 7 5 4 | 2 8 9
7 4 2 | 9 1 8 | 5 6 3
5 8 9 | 3 6 2 | 4 1 7
------+-------+------
8 6 7 | 1 2 5 | 3 9 4
2 5 3 | 6 4 9 | 8 7 1
4 9 1 | 8 7 3 | 6 2 5

974236158638591742125487936316754289742918563589362417867125394253649871491873625

'''Solution'''

974236158638591742125487936316754289742918563589362417867125394253649871491873625

'''Pass Condition'''

Unique Solution Found

----

== Last Empty Square ==

This puzzle requires only a single value to be placed on the grid in order to reach the unique solution: a ‘3’ in square r5c5.

'''Givens'''

2 5 6 | 4 8 9 | 1 7 3
3 7 4 | 6 1 5 | 9 8 2
9 8 1 | 7 2 3 | 4 5 6
------+-------+------
5 9 3 | 2 7 4 | 8 6 1
7 1 2 | 8 . 6 | 5 4 9
4 6 8 | 5 9 1 | 3 2 7
------+-------+------
6 3 5 | 1 4 7 | 2 9 8
1 2 7 | 9 5 8 | 6 3 4
8 4 9 | 3 6 2 | 7 1 5

2564891733746159829817234565932748617128.6549468591327635147298127958634849362715

'''Solution'''

256489173374615982981723456593274861712836549468591327635147298127958634849362715

'''Pass Condition'''

Unique Solution Found

----

== Naked Singles ==

This puzzle can be solved using only ‘Naked Singles’—also called ‘sole candidates’—which occur when a square has only one possible value remaining. The most obvious example of a Naked Single is the last square in any box, column, or row.

'''Givens'''

3 . 5 | 4 2 . | 8 1 .
4 8 7 | 9 . 1 | 5 . 6
. 2 9 | . 5 6 | 3 7 4
------+-------+------
8 5 . | 7 9 3 | . 4 1
6 1 3 | 2 . 8 | 9 5 7
. 7 4 | . 6 5 | 2 8 .
------+-------+------
2 4 1 | 3 . 9 | . 6 5
5 . 8 | 6 7 . | 1 9 2
. 9 6 | 5 1 2 | 4 . 8

3.542.81.4879.15.6.29.5637485.793.416132.8957.74.6528.2413.9.655.867.192.965124.8

'''Solution'''

365427819487931526129856374852793641613248957974165283241389765538674192796512438

'''Pass Condition'''

Unique Solution

Naked Singles:

r1c2 => 6 r1c6 => 7 r1c9 => 9 r2c5 => 3
r2c8 => 2 r3c1 => 1 r3c4 => 8 r4c3 => 2
r4c7 => 6 r5c5 => 4 r6c1 => 9 r6c4 => 1
r6c9 => 3 r7c5 => 8 r7c7 => 7 r8c2 => 3
r8c6 => 4 r9c1 => 7 r9c8 => 3

----

== Hidden Singles ==

This puzzle requires ‘Hidden Singles’ to solve, which occur when a box, column, or row has only one possible square remaining for a given value.

'''Givens'''

. . 2 | . 3 . | . . 8
. . . | . . 8 | . . .
. 3 1 | . 2 . | . . .
------+-------+------
. 6 . | . 5 . | 2 7 .
. 1 . | . . . | . 5 .
2 . 4 | . 6 . | . 3 1
------+-------+------
. . . | . 8 . | 6 . 5
. . . | . . . | . 1 3
. . 5 | 3 1 . | 4 . .

..2.3...8.....8....31.2.....6..5.27..1.....5.2.4.6..31....8.6.5.......13..531.4..

'''Solution'''

672435198549178362831629547368951274917243856254867931193784625486592713725316489

'''Pass Condition'''

Unique Solution

Hidden Singles:

r3c1 => 8 r7c1 => 1 r2c7 => 3 r2c4 => 1
r1c7 => 1 r3c7 => 5 r6c2 => 5 r2c1 => 5
r4c6 => 1 r5c6 => 3 r4c1 => 3 r7c3 => 3
r5c4 => 2 r5c9 => 6 r5c5 => 4 r4c9 => 4
r8c7 => 7

----

== See Also ==

* [[Test Cases]]

Valid Test Cases - Revision history

Rooted: Created page with "These test cases should result in a valid puzzle, and potentially a unique solution. == Completed Puzzle == A case of ‘more than enough’, this puzzle has already..."