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HOLLYDOLL
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 Posted: Sat Sep 03, 2005 7:15 pm Post subject: BLKCOL TECHNIQUE |
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CAN'T UNDERSTAND THE SAMPLE PUZZLE THAT WAS TO HELP ME UNDERSTAND AND USE THE TECHNIQUE. HELP.
243 789 651
679 451 823
1XX 236 794
592 XXX X47
8XX 924 5X6
4XX XX5 982
3XX 54X X79
7X4 X9X X6X
92X XX7 4XX
I WOULD LOVE IT EXPLAINED. THANKS. |
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David Bryant
Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado
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| Posted: Sun Sep 04, 2005 5:27 am Post subject: This puzzle can't be solved |
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I'm just curious, Holly -- where did you get this particular puzzle? Are you certain you entered all the numbers correctly? I guess that really doesn't matter, because this array will serve to illustrate the technique you're asking about. But the fact is that there is no valid solution to the puzzle you've posted. To understand why, just follow the (rather long) explanation that follows.
First, there are a couple of very obvious moves to be made immediately -- one must place the number "7" in r6c5 and then in r5c8. After making these two simple moves we reach the following position:
| Code: |
2 4 3 7 8 9 6 5 1
6 7 9 4 5 1 8 2 3
1 5/8 5/8 2 3 6 7 9 4
5 9 2 1/3/6/8 1/6 3/8 1/3 4 7
8 1/3 7 9 2 4 5 1/3 6
4 1/3/6 1/6 1/3/6 7 5 9 8 2
3 1/6/8 1/6/8 5 4 2/8 1/2 7 9
7 1/5/8 4 1/3/8 9 2/3/8 1/2/3 6 5/8
9 2 1/5/6/8 1/3/6/8 1/6 7 4 1/3 5/8
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Now we can apply the "Block on Column" interaction technique. Focus your attention on the first block of the middle row (the intersection of rows 4, 5, & 6 with columns 1, 2, & 3). Clearly we cannot place a "6" in this box unless it appears in either column 2 or 3. That means we can eliminate the possibility r6c4=6; r6c4 can only contain the possible values {1,3}.
Now look at row 7 and think about the first box in the bottom row (the intersection of rows 7, 8, & 9 with columns 1, 2, & 3). We cannot place the number "6" in row 7 unless it appears in this box. So we know that either r7c2=6 or else r7c3=6. This allows us to eliminate the possibility r9c3=6, leaving the only possible values in that cell as {1, 5, 8}.
Now look at the {5, 8} pairs in r3c2 & r3c3, and in r8c9 & r9c9. These are linked with each other via two cells (r8c2 & r9c3) in the first box in the bottom row. We don't know whether "5" or "8" goes in r3c2. But whichever value we put there, it forces all the rest of the values in the chain r2c2 - r8c2 - r8c9 - r9c9 - r9c3 - r3c3. This chain might read 8 - 5 - 8 - 5 - 8 - 5, or it might read 5 - 8 - 5 - 8 - 5 - 8. Either way we can be certain that these six cells contain only the values [5, 8]. In particular, the cells r8c2 & r9c3 must contain a {5, 8} pair, and we can eliminate the possible value "8" in r7c2 & r7c3. But then we're left with only one possible spot to put the number "8" in row 7. At this point the matrix looks like this:
| Code: |
2 4 3 7 8 9 6 5 1
6 7 9 4 5 1 8 2 3
1 5/8 5/8 2 3 6 7 9 4
5 9 2 1/3/6/8 1/6 3/8 1/3 4 7
8 1/3 7 9 2 4 5 1/3 6
4 1/3/6 1/6 1/3 7 5 9 8 2
3 1/6 1/6 5 4 2/8 1/2 7 9
7 5/8 4 1/3/8 9 2/3/8 1/2/3 6 5/8
9 2 5/8 1/3/6 1/6 7 4 3 5/8
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The following moves are forced by the "sole candidate" rule.
r7c6=8
r7c7=2
r4c6=3
r4c4=8
r8c4=1
r4c7=1
r5c8=3
r5c2=1
After making these moves our matrix looks like this:
| Code: |
2 4 3 7 8 9 6 5 1
6 7 9 4 5 1 8 2 3
1 5/8 5/8 2 3 6 7 9 4
5 9 2 8 6 3 1 4 7
8 1 7 9 2 4 5 3 6
4 1/6 1/6 1 7 5 9 8 2
3 1/6 1/6 5 4 8 2 7 9
7 5/8 4 1/3/8 9 2/3/8 1/2/3 6 5/8
9 2 5/8 6 1 7 4 3 5/8
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But now it's apparent that a solution is impossible, because there's nowhere to put the "3" in row 6 (or in the first box of the middle row, whichever way you want to look at it).
Whew! I hope that helped. dcb  |
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