## Bi-diagonal puzzle?

For fans of Killer Sudoku, Samurai Sudoku and other variants

### Bi-diagonal puzzle?

If it has a condition that :
Code: Select all
`ABCDEFGHIIABCDEFGHHIABCDEFGGHIABCDEFFGHIABCDEEFGHIABCDDEFGHIABCCDEFGHIABBCDEFGHIAABCDEFGHIBCDEFGHIACDEFGHIABDEFGHIABCEFGHIABCDFGHIABCDEGHIABCDEFHIABCDEFGIABCDEFGH`

A has 1~9.
B,C,...,H,I, too.

But the row and colume don't need.
Is this type interesting?
Eioru

Posts: 182
Joined: 16 August 2006

So you have diagonals (both left- and right-slanting), but no rows or columns. What about boxes?

Bill Smythe
Smythe Dakota

Posts: 564
Joined: 11 February 2006

This cylindrical variant is equivalent to a latin square, where one group of diagonals is mapped to rows and the other ones to columns. So this variant is another point of view to latin squares. Something could be not so easy to spot as in latin squares. If you like symmetries you can get some nice puzzle which wouldn't be symmetrical in classic latin squares.

Uwe
Pyrrhon

Posts: 240
Joined: 26 April 2006

Smythe Dakota wrote:So you have diagonals (both left- and right-slanting), but no rows or columns. What about boxes?

Bill Smythe

Yes, it have box.
Others are same as normal 9x9 sudoku.
Eioru

Posts: 182
Joined: 16 August 2006

Okay with boxes it becomes more interesting. Here an example

Uwe

Pyrrhon

Posts: 240
Joined: 26 April 2006

I don't know if it's a puzzle solvable using pen and paper only, but there is a simple way to convert it to a toroidal jigsaw sudoku puzzle with disconnected regions...

First, we convert the cells coordinates as following:

... and then we can create the following jigsaw puzzle...

"Traditional" techniques such as LOL would be easier to spot here... But I would still appreciate if somebody could post a walkthrough here...
udosuk

Posts: 2698
Joined: 17 July 2005

I have here a walk through the un-transformed puzzle. It is possible and in all likelihood that not all steps are necessary. I hope I have no mistake in writing.
Naked and Hidden Singles are skipped
Box-Diagonal interaction between B5 and diagonal R1C9-R9C1 => R1C9, R2C8, R3C7 <> 4
Pointing Pair R3C4-R7C8 in diagonal R1C2-R9C1 => R1C5, R2C4, R7C9, R9C7 <> 4
Box-Diagonal interaction between B2 and diagonal R1C6-R9C5 => R4C3, R5C2, R6C1 <> 4
Box-Diagonal interaction between B4 and diagonal R1C7-R9C6 => R7C4 <> 4
Box-Diagonal interaction between B8 and diagonal R1C4-R9C5 => R4C1 <> 4
Diagonal-Box interaction between diagonal R1C-R9C7 => R7C7, R8C9, R9C8, R9C9 <> 6
Pointing Pair R3C2-R7C6 in diagonal R1C9-R9C8 => R1C3, R3C1, R8C6 <> 6
Box-Diagonal interaction between B8 and diagonal R1C3-R9C4 => R5C8, R6C7 <> 6
Pointing Pair R4C7-R6C8 in group B6 => R1C4, R9C2 <> 6
Box-Cell Interaction of B1 and R6C7 => R6C7 <> 2
Box-Cell Interaction of B1 and R7C7 => R7C7 <> 8
Box-Cell Interaction of B3 and R7C3 => R7C3 <> 7
Box-Cell Interaction of B6 and R1C3 => R1C3 <> 7
Box-Cell Interaction of B1 and R7C8 => R7C8 <> 7
Box-Diagonal interaction between B9 and diagonal R1C1-R9C9 => R3C3 <> 7
Naked Pair 5 and 8 in B9 => R2C3, R7C9, R9C1, R9C7, R9C8, R9C9 <> 5, 8
Diagonal-Box interaction between diagonal R1C1-R9C9 and B1 => R1C3, R2C1, R3C1, R3C2 <> 3
Naked Quadruple 2, 3, 6, 9 in B6
Pointing Pair R3C6-R7C2 in diagonal R1C8-R9C9 => R2C6, R8C2 <> 6
Box-Cell Interaction of B3 and R7C4 => R7C4 <> 2
Box-Cell Interaction of B9 and R4C3 => R4C3 <> 3
Diagonal-Cell Interaction of diagonal R1C3-R9C4 and R2C1 => R2C1 <> 5
Diagonal-Cell Interaction of diagonal R1C6-R9C7 and R6C2 => R6C2 <> 5, 8
Generalized X-Wing with strong links in B2 B6 and weak links in diagonals R1C3-R9C2 and R1C4-R9C3 => R7C9 <> 6
Box-Diagonal interaction between B5 and diagonal R1C1-R9C9 => R1C1 <> 6
Box-Diagonal interaction between B1 and diagonal R1C4-R9C5 => R6C8 <> 6
Box-Diagonal interaction between B1 and diagonal R1C3-R9C4 => R5C8, R9C4 <> 2
Box-Diagonal interaction between B4 and diagonal R1C6-R9C7 => R1C6 <> 5
Hidden Pair 2, 4 in B3
Pointing Pair R1C9-R9C8 in diagonal R1C9-R9C8 => R1C7 <> 3
Box-Diagonal interaction between B3 and diagonal R1C9-R9C1 => R7C3, R8C2 <> 3
Turbot Fish with 3, strong links in B3 and B9 => R5C2 <> 3
Turbot Fish with 5, strong links in diagonals R1C3-R9C2 and R1C8-R9C9 => R7C3 <> 5
Turbot Fish with 8, strong links in B5 and B9 => R4C2 <> 8
Box-Diagonal interaction between B4 and diagonal R1C6-R9C7 => R1C6 <> 8
Pointing Pair R1C8-R6C4 in diagonal R1C8-R9C7 => R1C9 <> 8
Box-Diagonal interaction between B3 and R1C8-R9C9 => R3C6 <> 8
Generalized X-Wing with 8, strong links in diagonals R1C6-R9C5, R1C8-R9C7 and weak links in B3 and diagonal R1C9-R9C1 => R8C2 <> 8

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Pyrrhon

Posts: 240
Joined: 26 April 2006