Fishing expedition ended, but keep your rods ready

[Ruud]

To all fishermen & fisherwomen:

I'm sorry to announce that our little expedition has ended.

I hope you had a good week and caught some nice fish. Since this coincided with the opening of the fishing season, don't stow away your fishing gear, because there will be more to catch.

The addition of APE in SudoCue will have an impact on Nightmare difficulties later this season. New puzzles are being generated and they will be rated with the new engine.

As for this week: No special theme, unless you count variation as a theme. Almost every Nightmare for this week requires 8 or more non-basic techniques.

Have a nice week!

Ruud

[David Bryant]

Hi, Ruud! I really enjoyed today's puzzle, so I thought I would comment on it.

I know you said that SudoCue doesn't employ double-implication chains. But I think it does use a couple of special types of DIC -- the XY-Wing in previous versions, and the "APE" in the versions you released recently (I've installed 1.3.1 -- need to download 1.4.0 sometime soon).

Anyway, after doing the basic stuff (unique column/row, naked and hidden subsets, box/line interactions) I arrived at this position.

Code: Select all

123567 2356   8     36   157    9     34    25   347
 1357  359    19    2     4    1357   6     8     37
23567   4    235    8     57   3567   1     25    9
  9    2568  245    15    3    145    58    7     56
 356    1     35    7     2     8     9     4    356
 358    7    345    9     6     45   358    1     2
  4    589    6     15   1579  157    2     3    158
 135   359    7     36    8     2     45    69   145
12358 23589   19    4    159    36    7     69   158

At this point the puzzle is ready to crack wide open. All we need are a couple of double-implication chains.

First we see a "4-star constellation":

A. r2c3 = 1 ==> r1c5 = 1
B. r2c3 = 9 ==> r9c3 = 1

We conclude that r9c5 <> 1. Now, since the "1" in row 7 must clearly lie in the bottom center 3x3 box, we can also eliminate "1" at r7c9. The grid looks like this.

Code: Select all

123567 2356a  8     36   157    9     34    25   347
 1357  359    19    2     4    1357   6     8     37
23567   4    235    8     57   3567a  1     25    9
  9    2568  245    15    3    145    58    7     56a
 356    1     35    7     2     8     9     4    356
 358    7    345    9     6     45   358    1     2
  4    589    6     15   1579  157    2     3     58*
 135   359    7     36    8     2     45    69   145
12358 23589   19b   4     59b   36X   7     69B  158b

And now a beautiful 6-star constellation strikes the final blow:

A. r7c9 = 5 ==> r4c9 = 6 ==> r1c2 = 6 ==> r3c6 = 6
B. r7c9 = 8 ==> {1, 5, 9} triplet in row 9 ==> r9c8 = 6

We conclude that r9c6 = 3, and the rest is a piece of cake.

So much for my approach. Let's see what SudoCue does. Interestingly enough, the program arrives at the first position I have illustrated above.

Code: Select all

123567 2356   8     36   157    9     34    25   347
 1357  359    19    2     4    1357   6     8     37
23567   4    235    8     57   3567   1     25    9
  9    2568  245    15    3    145    58    7     56
 356    1     35    7     2     8     9     4    356
 358    7    345    9     6     45   358    1     2
  4    589    6     15   1579  157    2     3    158
 135   359    7     36    8     2     45    69   145
12358 23589   19    4    159    36    7     69   158

Now the program announces the following moves.

1. Aligned Pair Eliminations for r6c1 and r6c3.

r6c1 = 5 ==> r6c6 = 4
r6c1 = 5 ==> r5c3 = 3

But now there are no candidates for r6c3. Therefore r6c1 <> 5. I would call this a "4-star constellation."

2. Finned Swordfish found for digit 1.

This, apparently, is the same thing as the 4-star constellation I found in columns 3 & 5, eliminating the "1" at r9c5.

3. Box 8 only has candidates for Digit 1 in Row 7.

4. One candidate for Digit 3 eliminated by a template check.

This is a "Nishio" move.

r8c1 = 3 ==> r9c6 = 3 ==> r1c4 = 3 ==> r2c9 = 3 ==> r6c7 = 3
(r8c1 = 3 & r1c4 = 3 & r2c9 = 3) ==> r3c3 = 3

But now there's no way left to place a "3" in Box 4, so r8c1 = 3 is seen to be impossible.

5. Row 8 found a Naked Triple with Digits {1, 4, 5}

Just so we don't lose track, here's what the grid looks like now.

Code: Select all

123567 2356   8     36   157    9     34    25   347
 1357  359    19    2     4    1357   6     8     37
23567   4    235    8     57   3567   1     25    9
  9    2568  245    15    3    145    58    7     56
 356    1     35    7     2     8     9     4    356
  38    7    345    9     6     45   358    1     2
  4    589    6     15   1579  157    2     3     58
  15    39    7     36    8     2     45    69   145
12358 23589   19    4     59    36    7     69   158

6. R9C3 causes an XY-Wing eliminating Digit 5

r9c3 = 1 ==> r8c1 = 5; r9c3 = 9 ==> r9c5 = 5

We can eliminate "5" at r9c1 and at r9c2.

7. Coloring value 5 found a connected pair.

This is a "fork" from r4c4/r6c4 and r9c5/r9c9. We can eliminate the "5" at r4c9.

And now, with r4c9 = 6, the rest of the puzzle crumbles. Notice that the conclusion r9c6 = 3 (the result of the "6-star constellation" described above) follows very quickly after r5c9 = 6.

In thinking about this, it appears that the "APE" move is not really required to get to r4c9 = 6. And even though my approach seems much different from the path SudoCue took, they both in fact depend on the way the digit "6" is distributed to crack the puzzle wide open. dcb