## This is a hard one

Post the puzzle or solving technique that's causing you trouble and someone will help

### This is a hard one

This sudoku is quite hard.

Code: Select all
`    1 0 0   0 7 0   0 0 5  0 2 0   0 0 0   0 6 0  0 0 3   0 0 0   4 0 0    0 0 0   4 0 3   0 0 0  6 0 0   0 5 0   0 0 4  0 0 0   2 0 6   0 0 0    0 0 9   0 0 0   7 0 0  0 1 0   0 0 0   0 8 0  7 0 0   0 3 0   0 0 9  *-----------*|1..|.7.|..5||.2.|...|.6.||..3|...|4..||---+---+---||...|4.3|...||6..|.5.|..4||...|2.6|...||---+---+---||..9|...|7..||.1.|...|.8.||7..|.3.|..9|*-----------*`
ohanian

Posts: 2
Joined: 20 May 2006

Code: Select all
` *-----------* |1..|.7.|..5| |.2.|...|.6.| |..3|...|4..| |---+---+---| |...|4.3|...| |6..|.5.|..4| |...|2.6|...| |---+---+---| |..9|...|7..| |.1.|...|.8.| |7..|.3.|..9| *-----------*`

This is another invalid puzzle, as it has multiple solutions. Simple Sudoku says "too many solutions to count"

One of the solution paths takes us here:
Code: Select all
` *-----------------------------------------* | 1   4   6   | 3   7   2   | 8   9   5   | | 9   2   5   | 8   4   1   | 3   6   7   | | 8   7   3   | 9   6   5   | 4   1   2   | |-------------+-------------+-------------| | 2   9   7   | 4   8   3   | 1   5   6   | | 6   8   1   | 7   5   9   | 2   3   4   | | 35  35  4   | 2   1   6   | 9   7   8   | |-------------+-------------+-------------| | 35  35  9   | 6   2   8   | 7   4   1   | | 4   1   2   | 5   9   7   | 6   8   3   | | 7   6   8   | 1   3   4   | 5   2   9   | *-----------------------------------------*`

The puzzle is almost finished, but look in r6c1, r6c2, r7c1 and r7c2. Those four cells are all 3,5 and occupy 2 rows, 2 columns, and 2 boxes. That's a deadly pattern.

The puzzle can be solved two ways from there:

Code: Select all
`  *-----------* |146|372|895| |925|841|367| |873|965|412| |---+---+---| |297|483|156| |681|759|234| |354|216|978| |---+---+---| |539|628|741| |412|597|683| |768|134|529| *-----------* and  *-----------* |146|372|895| |925|841|367| |873|965|412| |---+---+---| |297|483|156| |681|759|234| |534|216|978| |---+---+---| |359|628|741| |412|597|683| |768|134|529| *-----------*`

Whenever you see a deadly pattern like that you will know the puzzle has multiple solutions. If you can safely assume that there is a unique solution then you can sometimes make exclusions based on the knowledge that a deadly pattern cannot be there.

See "Unique Rectangles"
Sped

Posts: 126
Joined: 26 March 2006

### Re: This is a hard one

ohanian wrote:This sudoku is quite hard.
Code: Select all
`*-----------*|1..|.7.|..5||.2.|...|.6.||..3|...|4..||---+---+---||...|4.3|...||6..|.5.|..4||...|2.6|...||---+---+---||..9|...|7..||.1.|...|.8.||7..|.3.|..9|*-----------*`

Sped wrote:This is another invalid puzzle, as it has multiple solutions. Simple Sudoku says "too many solutions to count"

Try this one.
Easy, but valid...
Code: Select all
` 1 . . | . 7 . | . . 6 . 2 . | . . . | . 4 . . . 3 | . . . | 8 . .-------+-------+------- . . . | 4 . 2 | . . . 6 . . | . 5 . | . . 1 . . . | 8 . 6 | . . .-------+-------+------- . . 8 | . . . | 4 . . . 3 . | . . . | . 2 . 7 . . | . 9 . | . . 5`

JPF
JPF
2017 Supporter

Posts: 3754
Joined: 06 December 2005
Location: Paris, France

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