some others that are not so obvious (X-Wing in the "8"s, XY-Wing rooted in
r6c6, a couple of connected pairs) I arrived at this position.
Code: Select all
79 6 1 28 5 4 3 79 28
2 8 357 13 179 179 157 6 4
379 4 357 123 178 6 15789 1579 27
157 3 8 15 179 2 79 4 6
4 57 6 58 3 789 2 579 1
157 9 2 46 46 17 57 8 3
6 2 9 7 48 13 48 13 5
8 157 37 46 146 135 147 2 9
35 157 4 9 2 1358 6 137 78that assumption there must be a "1" at r8c5. And that is enough to
crack the rest wide open.
What if we don't want to make that assumption? One way to proceed works
fairly quickly,like this ("double-implication chain").
First, if we set r7c5 = 8 we will have the {1, 7, 9} triplet in r2c5, r3c5,
& r4c5, forcing the possibilities {4, 6} at r8c5, and guaranteeing that
any solution that can now be found will not be unique. So let's assume
that r7c5 = 8, and look for a contradiction.
A. r7c5 = 8 ==> "1" in r7c6, r8c6, or r9c6 ==> r6c6 = 7 ==> r2c6 = 9 ==> r5c6 = 8
B. r7c5 = 8 ==> r1c4 = 8 ==> r1c9 = 2 ==> r3c9 = 7 ==> r1c8 = 9
But now it's impossible to place a "9" in row 5. So r7c5 <> 8, and we
must have r7c5 = 4. And this is enough to solve the puzzle. dcb