Solving
this configuration using Sudoku Assistant does
require almost-locked sets. I get:
Done! (46 steps) AaMw
562 893 147
738 641 592
491 752 683
287 365 419
649 218 375
153 479 268
975 126 834
314 587 926
826 934 751
The following is not meant to be "a solution". Rather, it itemizes
all of "basic" logical conclusions that can be drawn from this
PARTICULAR configuration:
Strong Chains: 1 2 3 4 5 6 7 8 9 10 11 12 13 14
60 cells left to solve; 21 clues; 500 tidbits of information
103 almost-locked sets (Y)
(ooh!)
r3c4 ISN'T 2: weakly linked to two almost-locked sets already weakly linked by 8: r2c6 r3c6 and r1c4 r4c4 r9c4
r7c3 ISN'T 1: weakly linked to two almost-locked sets already weakly linked by 4: r8c1 r8c2 r8c3 and r3c3 r4c3
r8c3 ISN'T 1: weakly linked to two almost-locked sets already weakly linked by 7: r3c3 and r7c3 r8c1 r8c2
r7c1 ISN'T 1: weak link to almost-locked sets r4c3 and r7c3 r8c1 r8c2 r8c3 mutually doubly-linked by 4,7
r7c2 ISN'T 1: weak link to almost-locked sets r4c3 and r7c3 r8c1 r8c2 r8c3 mutually doubly-linked by 4,7
r7c1 ISN'T 5: weak link to almost-locked sets r4c3 and r7c3 r8c1 r8c2 r8c3 mutually doubly-linked by 4,7
r7c2 ISN'T 5: weak link to almost-locked sets r4c3 and r7c3 r8c1 r8c2 r8c3 mutually doubly-linked by 4,7
r7c1 ISN'T 1: weak link to almost-locked sets r7c3 r8c1 r8c2 r8c3 and r3c3 r4c3 mutually doubly-linked by 4,7
r7c2 ISN'T 1: weak link to almost-locked sets r7c3 r8c1 r8c2 r8c3 and r3c3 r4c3 mutually doubly-linked by 4,7
r7c1 ISN'T 5: weak link to almost-locked sets r7c3 r8c1 r8c2 r8c3 and r3c3 r4c3 mutually doubly-linked by 4,7
r7c2 ISN'T 5: weak link to almost-locked sets r7c3 r8c1 r8c2 r8c3 and r3c3 r4c3 mutually doubly-linked by 4,7
r6c3 ISN'T 1: weak link to almost-locked sets r7c3 r8c1 r8c2 r8c3 and r3c3 r4c3 mutually doubly-linked by 4,7
100 almost-locked sets (X)
(oooooooooh; amazingly, nothing here, though...)
Checking strong chains
14 strong chains
r3c4 ISN'T 2: r3c4#2 is incompatibly weakly linked to 2(b) involving nodes r1c4#3 chain 2(B) and r1c6#3 chain 2(b) via ALS r1c4 r2c6 r3c6
r3c4 ISN'T 2: r3c4#2 is incompatibly weakly linked to 2(b) involving nodes r1c4#3 chain 2(B) and r1c4#8 chain 2(b) via ALS r2c6 r3c6
r3c4 ISN'T 2: r3c4#2 is incompatibly weakly linked to 2(b) involving nodes r1c4#3 chain 2(B) and r2c5#4 chain 2(b) via ALS r1c4 r1c6 r2c6 r3c6
r7c6 ISN'T 2: r7c6#2 is incompatibly weakly linked to 2(B) involving nodes r1c4#8 chain 2(b) and r9c2#4 chain 2(B) via ALS r9c4 r9c6
r7c3 ISN'T 1: r7c3#1 is incompatibly weakly linked to 2(b) involving nodes r9c2#4 chain 2(B) and r8c3#4 chain 2(b) via ALS r3c3 r4c3
r7c6 ISN'T 2: r7c6#2 is incompatibly weakly linked to 2(B) involving nodes r1c4#8 chain 2(b) and r8c5#4 chain 2(B) via ALS r9c4 r9c6
r7c6 ISN'T 2: r7c6#2 is incompatibly weakly linked to 2(B) involving nodes r1c4#8 chain 2(b) and r9c4#2 chain 2(B) block 8
(note the chain/ALS combo here)
Checking for weak links
51 weak links
475 weak corners
(whew!!)
r7c1 ISN'T 5: weak corner eliminated by both 2(B) and 2(b)--3(C)
r7c1 ISN'T 5: weak corner eliminated by both 2(B) and 2(b)--5(e)
r3c9 ISN'T 2: weak corner eliminated by both 2(b) and 2(B)--7(G)
r7c3 ISN'T 1: weak corner eliminated by both 2(B) and 2(b)--8(h)
r3c9 ISN'T 2: weak corner eliminated by both 2(b) and 2(B)--13(M)
r7c1 ISN'T 5: weak corner eliminated by both 3(C) and 3(c)--2(B)
r7c1 ISN'T 5: weak corner eliminated by both 3(C) and 3(c)--6(f)
r7c1 ISN'T 1: weak corner eliminated by both 3(C) and 3(c)--12(l)
r7c1 ISN'T 5: weak corner eliminated by both 5(e) and 5(E)--2(B)
r7c1 ISN'T 5: weak corner eliminated by both 6(f) and 6(F)--3(C)
r3c9 ISN'T 2: weak corner eliminated by both 7(G) and 7(g)--2(b)
r7c3 ISN'T 1: weak corner eliminated by both 8(h) and 8(H)--2(B)
r7c1 ISN'T 1: weak corner eliminated by both 12(l) and 12(L)--3(C)
r3c9 ISN'T 2: weak corner eliminated by both 13(M) and 13(m)--2(b)
(Again, some duplicates here -- the idea is to show ALL possible
implications. These somehow involve ALS, but I don't know how from this)
Chain 1: r1c1#5(a) r1c1#6(A) r1c2#5(A) r1c2#6(a)
Chain 2: r1c4#3(B) r1c6#3(b) r1c6#4(B) r1c8#4(b) r1c4#8(b) r1c8#8(B) r2c5#4(b) r2c7#4(B) r5c2#4(b) r9c2#4(B) r4c3#4(B) r8c3#4(b) r4c1#3(B) r4c4#3(b) r4c3#7(b) r4c7#4(b) r4c4#9(B) r9c4#9(b) r6c6#3(B) r5c8#4(B) r8c5#4(B) r6c6#9(b) r9c6#4(b) r9c6#9(B) r9c2#2(b) r9c4#2(B)
Chain 3: r2c1#9(c) r7c1#9(C) r3c2#9(C) r7c2#9(c) r3c8#9(c)
Chain 5: r2c1#7(e) r2c5#7(E)
Chain 6: r2c8#5(f) r2c8#9(F)
Chain 7: r3c8#3(g) r3c9#3(G) r7c3#3(g) r7c8#3(G) r8c9#3(g)
Chain 8: r3c3#1(h) r3c3#7(H)
Chain 12: r8c2#1(l) r8c2#5(L)
Chain 13: r8c5#6(m) r8c9#6(M)
Chain 14: r9c8#1(n) r9c9#1(N) r9c8#5(N) r9c9#5(n)
(Chain 2 is the one that takes care of a lot of what Jeff suggested. Quite a monster.)
