please help solve this 7x7 puzzel

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please help solve this 7x7 puzzel

Postby twerkman » Sun Mar 17, 2013 10:05 am

help me solve this puzzel for my kid

it's a 7 x 7 square and you have to use the numbers from 1 to 7 and the same number should not come twice in the same line, diagonaal and column.

1 . . . . . .
. . . . . . 3
. . . . 4 . .
. . 5 . . . .
. . . 2 . . .
. . . . . 7 .
. 6 . . . . .


We think that there is a fault somewhere.... please help solve it

Thank you
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Re: please help solve this 7x7 puzzel

Postby twerkman » Sun Mar 17, 2013 3:15 pm

I added an attachment in word, more easy to fill.

Thanks
Attachments
7x7.docx
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7x7 Latin Square X puzzle

Postby tarek » Sun Mar 17, 2013 4:39 pm

multiple solutions ..... That means that you can solve this puzzle with the constraints you mentioned but that solution is not unique.
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Re: 7x7 Latin Square X puzzle

Postby Smythe Dakota » Mon Mar 18, 2013 7:32 am

Any time you try a puzzle from an unknown source, and naively assume uniqueness, if it seems to be an unusually difficult puzzle, it's probably because you've solved as much as can be solved, with multiple possibilities for most or all of the remaining cells. Beware!

Bill Smythe
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Postby Pat » Mon Mar 18, 2013 3:29 pm

twerkman wrote:

    it's a 7 x 7 square

    you have to use the numbers from 1 to 7

    the same number should not come twice in the same
    • row
    • diagonaal
    • column
Code: Select all

1 . . . . . .
. . . . . . 3
. . . . 4 . .
. . 5 . . . .
. . . 2 . . .
. . . . . 7 .
. 6 . . . . .



We think that there is a fault somewhere....

suspect additional houses
= jigsaw boxes
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Re:

Postby blue » Tue Mar 19, 2013 10:19 am

If "diagonal" was intended to mean "any diagonal", not just the main diagonals, then there is just one solution.

If the diagonals are the "extended" kind (with length=7), then the puzzle can be solved easily with triples & pairs. If they're the "short" diagonals, with the only the requirement that no number appears twice, then it's much harder to solve, but there's still only one solution.

Actually any filled grid (against an empty clue set) that satisfies the "short diagonals" condition, also has no matches (and so all 7 numbers) on the extended diagonals. I don't know if that's easily proved or not.

Blue.
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Re: please help solve this 7x7 puzzel

Postby HATMAN » Thu Mar 21, 2013 3:18 pm

Perhaps a proof by induction starting with a 3*3?
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Re: please help solve this 7x7 puzzel

Postby tarek » Fri Mar 22, 2013 5:41 pm

Brilliant Blue ....

However

These puzzles should be designed as a toroid and therefore a square puzzle with lines having an even number of cells would have been more aesthetically pleasing because you you can leave the diagonals open ended and successfully form the toroidal puzzle. (This comes from work done on the Fairy chess puzzles :D :D :D )
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