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August 14 puzzle grade
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Max Beran



Joined: 11 Aug 2005
Posts: 9
Location: Oxfordshire, UK

PostPosted: Wed Aug 24, 2005 12:35 am    Post subject: Reply with quote

Terry

But you have changed the puzzle. We were given a "7" at r5c7 in the original layout and you have changed that.

Someone-somewhere - do you have a solution as all my attempts to bifurcate have led nowhere?
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Max Beran



Joined: 11 Aug 2005
Posts: 9
Location: Oxfordshire, UK

PostPosted: Wed Aug 24, 2005 12:54 am    Post subject: Reply with quote

I tried harder and found a solution. It can be reached by two "invalid" moves: r9c3=6 (this allows 47 cells to be completed); then r9c8=1 lets you finish the job.

Not much fun doing them this way though.
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Terry
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PostPosted: Wed Aug 24, 2005 1:14 am    Post subject: Oops! Reply with quote

You're right, I copied the original puzzle incorrectly. My old eyes have trouble with all those little numbers! I'll go back and try it again and let you know how I do.

A couple of points: As I said earlier, I just started doing these puzzles, so I don't know what you all mean by "invalid" moves or "bifurcating." Sometimes I get to a point where I have to approach the puzzle like a chess game and think through the logical consequences of alternate moves. This doesn't seem any less logical to me than other approaches.

Someone in this thread suggested writing a program to solve puzzles. I'm not a programmer, so I wouldn't have any idea how to do that, and even if I could, it doesn't sound like much fun to me. I'd rather think the puzzles through myself. But, to each his own.

BTW: I'm a person of the female persuasion. My name confuses people, but Terry can be a woman's name as well as a man's name.

I'll get back to you after I've had a go at the puzzle with the correct numbers.
Terry
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Terry
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PostPosted: Wed Aug 24, 2005 6:29 am    Post subject: Correct puzzle - I hope Reply with quote

How's this? Hope I copied it correctly this time. The incorrect one I did earlier was actually harder, but this one was certainly a challenge.

2 6 7 5 4 9 1 3 8
9 8 3 6 2 1 4 5 7
5 4 1 7 8 3 2 6 9
7 5 8 3 9 2 6 4 1
3 1 4 8 5 6 7 9 2
6 2 9 1 7 4 3 8 5
1 9 5 4 6 7 8 2 3
4 3 2 9 1 8 5 7 6
8 7 6 2 3 5 9 1 4

Terry
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someone_somewhere



Joined: 07 Aug 2005
Posts: 275
Location: Munich

PostPosted: Wed Aug 24, 2005 6:45 am    Post subject: Reply with quote

Terry,

That is nice. You give us the solution, and we should find probable the initial position with the minimum numbers. It should have around 17 such numbers.
That is a challange. Could be done ;-)

see u,
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Max Beran



Joined: 11 Aug 2005
Posts: 9
Location: Oxfordshire, UK

PostPosted: Wed Aug 24, 2005 1:34 pm    Post subject: Reply with quote

On further inspection it works out with just the one "invalid" move (by which I mean an arbitrary trial and error choice from among the candidates that has no logic behind it) not two as I suggested.

So the "6" at r9c3 remains as before the "invalid" move. But you then reach a point where you have 47 cells completed and a lot of cells with just the two candidates. There is an xy-chain starting at r1c1 and winding its way round to r5c9 that allows an elimination in r5c1. There may be other chains that have the same effect. This is a much more satisfactory way of proceeding to my purist mind which gives the result that Ms Terry already posted.

This is a good website for collecting together the principal logical techniques and giving them names:

http://www.simes.clara.co.uk/programs/sudokutechniques.htm

I wonder, someone-somewhere, if it is always the case that the minimum layouts like on the website you talked about need at least one trial and error move. This suggests another question; what is the minimum number of filled cells that produce a puzzle that can be solved by logic alone? That's another one for the mathematicians.
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Max Beran



Joined: 11 Aug 2005
Posts: 9
Location: Oxfordshire, UK

PostPosted: Thu Aug 25, 2005 12:57 am    Post subject: Reply with quote

I've answered my own question about whether puzzles with few cells filled in will tend to need trial and error at some point. The following puzzle has only 17 starter cells but can be completed with simple logic.

xxx|xxx|x12
xxx|x35|xxx
xxx|6xx|x7x
---------------
7xx|xxx|3xx
xxx|4xx|8xx
1xx|xxx|xxx
--------------
xxx|12x|xxx
x8x|xxx|x4x
x5x|xxx|6xx

Note that there are no 9's at all given here.
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Terry
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PostPosted: Fri Aug 26, 2005 5:15 am    Post subject: Max's 17-number, no 9s puzzle Reply with quote

Nice puzzle, Max. If I copied the darn thing right, this is what I get:

6 7 3 8 9 4 5 1 2
9 1 2 7 3 5 4 8 6
8 4 5 6 1 2 9 7 3
7 9 8 2 6 1 3 5 4
5 2 6 4 7 3 8 9 1
1 3 4 5 8 9 2 6 7
4 6 9 1 2 8 7 3 5
2 8 7 3 5 6 1 4 9
3 5 1 9 4 7 6 2 8

Terry
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someone_somewhere



Joined: 07 Aug 2005
Posts: 275
Location: Munich

PostPosted: Sat Aug 27, 2005 2:49 pm    Post subject: Reply with quote

hi,
At least 85% out of the 19197 known 17 cells Sudokus, can be solved by LOGIC.

For the 19197 "17 cells", see the page Minimum Sudoku:
http://www.csse.uwa.edu.au/~gordon/sudokumin.php

see u,
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dlg
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PostPosted: Wed Aug 31, 2005 4:10 am    Post subject: Re: sunday aug-14-2005 puuzzle Reply with quote

aardy wrote:
I think very hard puzzles have more than one solution.Has anyone ever gave a try.Kindly do try and post the result.


I think you're right. Try this one:

Published Alternate
solution solution

792 184 365 192 784 356
841 635 792 873 615 294
356 729 814 456 329 718

513 246 978 315 248 679
469 817 523 748 196 523
278 593 146 269 573 841

685 972 431 681 957 432
924 351 687 524 831 967
137 468 259 937 462 185
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dlg
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PostPosted: Wed Aug 31, 2005 4:14 am    Post subject: Re: sunday aug-14-2005 puuzzle Reply with quote

aardy wrote:
I think very hard puzzles have more than one solution.Has anyone ever gave a try.Kindly do try and post the result.


My spacing seems to have disappeared in my prior message, but if you separate them into 9x9 blocks, you'll get the idea.
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chobans



Joined: 21 Aug 2005
Posts: 39

PostPosted: Wed Aug 31, 2005 3:36 pm    Post subject: Reply with quote

r5c3 and r4c9 are fixed numbers. Your alternate solution changed those numbers. So the alternate solution is wrong.
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PostPosted: Wed Aug 31, 2005 11:39 pm    Post subject: Reply with quote

chobans wrote:
r5c3 and r4c9 are fixed numbers. Your alternate solution changed those numbers. So the alternate solution is wrong.


You're right. I really blew it.
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naz
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PostPosted: Sat Sep 03, 2005 6:58 pm    Post subject: August 14 puzzle grade Reply with quote

Hi dlg,

you nearly did it.Terry also made once same mistake.He corrected it when pointed out.I think second solution is almost certain.Try again and i am sure you will be able to get it.

I would also love to solve it now.

cheers,

naz
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