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net.flyer
Joined: 21 Dec 2005 Posts: 3 Location: Sammamish WA, USA

Posted: Thu Dec 22, 2005 8:02 am Post subject: Dec 21st game... 


xxx 7x8 xx3
8x4 36x 729
x73 xxx 6xx
xxx 24x 5x1
x27 xxx 83x
5x6 83x 9x2
xx5 x7x 29x
7x1 982 3x5
xxx 653 xx7
In the above game on Dec 21st, I was stumped at this point although I had all the possible number possibilites for the missing numbers (x). I asked for a hint and was given the number 8 for r3c9. When I plugged this number in, the rest of the board fell like a line of dominoes.
I've studied the above position and can't figure out how the answer for r3c9 can be determined by the given and solved numbers at that point. Can anyone explain how this number ( was determined? In the upper right square, I had position r3c8 also as a possible 8 along with 1,4 and 5 as possible answers along with r3c9 as either 4 or 8. It seems to me that r3c8 HAS to be solved before r3c9. 

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geoff h
Joined: 07 Aug 2005 Posts: 58 Location: Sydney

Posted: Thu Dec 22, 2005 9:12 am Post subject: 


Hi there,
Actually, there is no reason why you must sove for cell r3c8 before solving for cell r3c9. The idea is not to find where the 8 must go, but rather to eliminate the number 4.
To do this, you must first look closely at Column 8. There is a triplet of 4,6,7 in cell numbers r4c8, r6c8 and r8c8. Therefore, you can eliminate all other numbers 4,6 and 7 from all other cells in Column 8. In particular, you can remove the number 4 from cells r1c8 and r3c8.
Now, consider Row Number 1. Because we have eliminated 4 from cell r1c8, the only cell from Row 1 to place the number 4 is r1c7.
Then finally, you can consider Box No. 3 ( top righthand side ). Because we have placed 4 in cell r1c7, then cell r3c9 MUST be number 8.
And the puzzle should flow easily from there.
Cheers,
Geoff. 

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Steve R
Joined: 24 Oct 2005 Posts: 289 Location: Birmingham, England

Posted: Thu Dec 22, 2005 1:47 pm Post subject: Dec 21st game... 


The visual approach works as well.
Inspecting the middle topmost box shows that the 4 must occupy r3, so it is excluded from r3c8.
Steve 

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net.flyer
Joined: 21 Dec 2005 Posts: 3 Location: Sammamish WA, USA

Posted: Thu Dec 22, 2005 6:26 pm Post subject: Thanks for the insight... 


I've only been playing Sudoku for about 2 months now. The two methods above are very logical after the explanations, but I certainly didn’t see them when I was stumped and asked for the hint although I think I should have seen the triplet. In all the games I’ve played, I don’t think I’ve ever seen one where one number, r3c9 would be the key to the solution. If I counted right, when I was stumped, I had 42 slots filled (given plus solved). With r3c9 solved, the other 56 slots were filled as quickly as I could write. I’m wondering if I had been give a hint somewhere else on the board, would the solution to the puzzle have been as easy?
In other words, does a request for a hint provide the greatest chance to “run” the rest of the board or did it just work out that way in this puzzle?
Thanks for the answers above…
Net.flyer 

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