sultan vinegar wrote:With my (slightly more SK-loop like cover sets in b45) I miss out on the elimination of 4r4c8 though. As you say the eliminations are very interesting. Here it seems that there is the SK-loop like AMSLS in boxes 4,5,7,8 and the ALS in r12c7 which get stitched together and magically the truths balance because of the cells in r47c7. Is this just a freaky coincidence or is there a reason for it, hidden in the puzzle symmetries somewhere?
Platinum Blonde contains an almost-sk-loop logic set with at least four equivalents. The equivalents aren't as neat and pretty as with a true sk-loop, but the same principles hold.
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After hidden single r9c3=5
000000012000000003002300400001800005060070800000009000008500000900040500475006000 Platinum Blonde unmorphed
Plat [22,251] 58 Candidates,
0-rank all-cell truths
19 Truths = {12N7 4N12567 56N34 7N12567 8N34 9N4}
19 Links = {23r4 123r7 3c3 12c4 679c7 479b4 46b5 6b7 79b8}
0-rank almost-sk-loop truths
18 Truths = {4679R47 4679C34 12N7}
18 Links = {679c7 12n3 12n4 47n8 7n9 479b4 46b5 6b7 79b8}
0-rank almost-all-column truths
18 Truths = {4679C3489 58B3}
18 Links = {49r5 467r6 67r8 9r9 12n3 12n4 2347n8 37n9}
0-rank almost-all-row truths
21 Truths = {4R1247 679R12347 58B3}
21 Links = {4c26 6c157 7c167 9c257 12n34 2347n8 37n9}
0-rank almost-all-box truths
18 Truths = {123C7 1B578 23B4578 5B45 8B48}
18 Links = {23r4 123r7 3c3 12c4 5n16 6n1257 8n26 9n57}
Each of the above has the same 17 exclusions
17 Eliminations --> r6c57<>6, r6c17<>7, r9c57<>9, r47c8<>23, r2c4<>12, r1c3<>3,
r5c6<>4, r6c2<>4, r7c9<>1, r8c6<>7
Note that r4c8<>4 is not listed as an exclusion.
