2/19/06 Nightmare: It's beyond me!

[Paladin]

I clearly have no idea how to solve this puzzle. I was able to determine four answers, and then I don't seem to be able to locate anything (forcing chains, swordfish, X Wings, XY Wings, etc.) that would allow me to complete this puzzle. The start grid appears immediately below; the second grid shows the four answers that I found at r3c1, r8c1, r5c4, r7c5.

Code: Select all

+------------+-----------+------------+
|  .   .   . | .   9   . |  6   .   . |
|  .   .   . | 6   .   8 |  .   .   . |
|  .   8   . | .   .   . |  3   5   . |
+------------+-----------+------------+
|  2   .   6 | .   .   4 |  8   1   . |
|  .   3   . | .   1   . |  .   2   . |
|  .   1   8 | 2   .   . |  9   .   5 |
+------------+-----------+------------+
|  .   6   4 | .   .   . |  .   7   . |
|  .   .   . | 3   .   1 |  .   .   . |
|  .   .   5 | .   4   . |  .   .   . |
+------------+-----------+------------+

Grid containing my four answers:

+------------+-----------+------------+
|  .   .   . | .   9   . |  6   .   . |
|  .   .   . | 6   .   8 |  .   .   . |
|  6   8   . | .   .   . |  3   5   . |
+------------+-----------+------------+
|  2   .   6 | .   .   4 |  8   1   . |
|  .   3   . | 8   1   . |  .   2   . |
|  .   1   8 | 2   .   . |  9   .   5 |
+------------+-----------+------------+
|  .   6   4 | .   8   . |  .   7   . |
|  8   .   . | 3   .   1 |  .   .   . |
|  .   .   5 | .   4   . |  .   .   . |
+------------+-----------+------------+

Any assistance would be very much appreciated.

[Steve]

First note the pair (14) in box 2 cells r13c4. Taking this into account there are only two places for 5 in the first row (box 1 and cell r1c6). There are also only two places for 5 in the fifth row, cells r5c16. this finned X-Wing eliminates 5 from r2c1, leaving the possible entries as (79). The XY-Wing pivoted on this cell then places 4 in the sixth row.

Steve

[lac]

What I did was decide that the crucial question was 'Is r3c9' a 9.
If if wasn't, then you could conclude r1c9 was 27or8.

I first tried to get a contradiction by setting it to 9. no go. (unsurprising,
that is what the solution was.) Then I set r3c3 to 9 (it would have
to be ifr3c9 wasn't) and got a contradiction soon enough.

It wasn't the happiest time to have solving though. What did the rest
of you do?

Laura

[David Bryant]

1. Resolved top center 3x3 box into {2, 7}, {3, 5}, and {1, 4} pairs.
2. Found {1, 4, 9} triplet in row 3, setting r3c1 = 6.
3. Found hidden pair {1, 3} in r7c1 & r9c1, setting r8c1 = 8.
4. The "4" in column 1 lies in middle left 3x3 box.
5. r5c4 = 8 (unique horizontal); r7c5 = 8 (unique vertical)
6. Coloring on "5" reveals pair {7, 9} in r2c1.
7. Coloring on "6" reveals {2, 4, 9} in r8c9.
8. XY-Wing from r2c1 eliminates "4" at r6c8; r6c1 = 4 (unique horizontal).
9. The "7" in row 6 lies in middle center 3x3 box.
10. {5, 9} pair revealed in column 4 -- r9c4 = 7.
11. {3, 5} pair revealed in column 5 -- r7c5 = 8.
12. r8c7 = 5 (unique horizontal), revealing {1, 2} pair in r7c7 & r9c7.
13. Triplet {4, 7, 9} lies in row 2.

After these steps and the associated eliminations the puzzle looks like this.

Code: Select all

 57   2457  1237   14     9    35     6    48   12478
 79    25    123    6    35     8    47    49    12
  6     8    19    14    27    27     3     5    149
  2    579    6    59    35     4     8     1    37
 579    3    79     8     1    569   47     2    467
  4     1     8     2    67    367    9    36     5
 13     6     4    59     8    259   12     7    39
  8    279   279    3    26     1     5    469   49
 13    29     5     7     4    269   12   3689  3689

And now we find a very nice "5-star constellation" in r2c1, r3c3, r5c3, r5c7,
and r2c7:

A. r5c7 = 7 ==> r5c3 = 9 ==> r3c3 = 1
B. r5c7 = 4 ==> r2c7 = 7 ==> r2c1 = 9 ==> r3c3 = 1

Setting r3c3 = 1 is enough to crack the rest of the puzzle wide open. dcb