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