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# Sudoku

Wed 29 Nov, 2006 06:32 am
I know Sudoku is very popular right now. If they wanted the puzzles to reallt be challenging, why couldn't they design the grids so that there are no repeating digits in any of the diagonals?
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Type: Discussion • Score: 0 • Views: 1,036 • Replies: 12
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markr

1
Wed 29 Nov, 2006 03:25 pm
I would expect that to make solving easier. More constraints equals fewer choices.
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JGoldman10

1
Thu 30 Nov, 2006 11:46 am
No repeating digits in any daigonals would make solving the puzzles harder. There are 9! (nine factorial) possible ways to arrange the digits 1 to 9 withiout repeating.
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markr

1
Thu 30 Nov, 2006 07:43 pm
How does the fact that there are 9! non-repeating arrangements make solving the puzzles harder?

On a main diagonal there are (9*8*7)^3 arrangements that include repeated numbers.

9! = 362,880
(9*8*7)^3 = 128,024,064
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JGoldman10

1
Sun 3 Dec, 2006 08:35 pm
No repeating digits in any row, column or diagonal makes solving the puzzles harder.
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markr

1
Sun 3 Dec, 2006 11:23 pm
Asserting something doesn't make it true. What's the basis of your assertion? Explain why adding a contraint (thus reducing the potential number of solutions) makes solving the puzzle harder.
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Heliotrope

1
Mon 4 Dec, 2006 01:24 pm
Needles in haystacks.

Many needles makes it easier to find one.
Only one needle makes it very hard.
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markr

1
Mon 4 Dec, 2006 04:09 pm
Nice analogy, but incorrectly applied.

In both cases, there is one needle. Adding constraints reduces the size of the haystack.

It's harder to make puzzles (fewer possibilities), not harder to solve them.
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ebrown p

1
Mon 4 Dec, 2006 04:37 pm
I agree with JGoldman.

An additional constraint would make the puzzles more difficult to create. I see no reason why it would make the puzzles more difficult to solve.

Logically the opposite would be true since it would mean I could rule out more digits in more spaces. Since I could say "that box can't be an 8 because I know there is already an 8 in this diagonal" this constraint would be an advantage to me as the puzzle solver.

If you insist that would be harder, I would like to see a proof.
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markr

1
Mon 4 Dec, 2006 07:06 pm
Actually, you agree with me.
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ebrown p

1
Mon 4 Dec, 2006 07:38 pm
Right you are markr. I think my math skills are better than my reading skills.
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g day

1
Tue 5 Dec, 2006 05:52 am
I think you might find its not only difficult, its actually impossible to do. Just a gut feeling but the constraints are already very tight, and yes there might be a small solution set, of < 30 puzzles that fit this extra rule, but my gut is that might be none.

Anyone good enough at linear algebra to definitely prove or disprove this?
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Heliotrope

1
Sat 16 Dec, 2006 05:57 pm
markr wrote:
Nice analogy, but incorrectly applied.

In both cases, there is one needle. Adding constraints reduces the size of the haystack.

It's harder to make puzzles (fewer possibilities), not harder to solve them.

True.
I should have clarified myself.
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