by **Mike Barker** » Sat Apr 08, 2006 6:26 pm

I guess I'd rate your first puzzle as less difficult than #77 since my solver can solve this, but not #77. Here's the solution it came up with. It is still a work in progress and so I won't guarantee the solution. I've started to implement some of Ron's and Carcul's suggestions, but have a ways to go. I have the mutual exclusion rule implemented for ALS and nice loops and have all of the eliminations reported (although not very concisely). I still use "~" to show the discontinuity in a nice loop (although not necessary, I kind of like the added detail) and don't show the final link for discontinuous nice loops where the start and end nodes don't share a house (it's actually all of the cells where eliminations occur). Also I use the strong-link approach for X-cycles instead of X-wings, Turbot fish, etc. so, for example, two grouped strong links could be either a finned X-wing or a grouped Turbot fish depending on whether the loop is continuous or discontinuous. Finally, I use the generalized version of mYZ-wings (eg WXYZ-wing). All steps are logical (no T&E).

(Updated with MER algorithm)

Hidden Single: r3c6 => r3c6=1,r3c1<>1,r3c2<>1,r3c8<>1,r3c9<>1

Locked Column: r123c4 => r6c4<>9

Locked Column: r123c5 => r7c5<>4,r9c5<>4

Locked Column: r23c5 => r9c5<>8

Two Grouped Strong Links: r6c4=7=r8c4-7-r8c7=7=r56c7~7~ => r6c8<>7

WXYZ-wing: r12c4|r1c5, r2c7 => r2c5<>4,r1c8<>4,r1c9<>4

ALS xz-rule with A=2 cells: r5c79-3-r5689c8 => r4c8<>5,r4c8<>7,r4c9<>7

ALS xy-rule with B=5 cells: r12c4-3-r12379c5-7-r46c5|r456c6 => r6c4<>5,r6c4<>2,r8c7<>5,r8c7<>7

Locked Column Box: r1389c8|r137c9 => r5c8<>7,r5c9<>7

ALS xy-rule with B=2 cells: r28c7-5-r12c4-3-r8c4|r79c5 => r8c6<>2,r3c4<>9,r3c4<>3

ALS xy-rule with B=3 cells: r2c3457-4-r568c7-5-r5c9 => r2c9<>3

ALS xy-rule with B=2 cells: r1c4589-1-r2c79-5-r3c12389 => r3c5<>4

Hidden Single: r1c5 => r1c5=4,r1c1<>4

Nice Loop: r2c7-4-r6c7=4=r6c8-4-ALS:r89c8~5~ => r3c8<>5

Nice Loop: r23c9=4=r7c9-4-ALS:r7c56|r9c5|r8c4-3-r1c4-9-r1c8=9=r3c8~9~r23c9 => r3c8<>4

Nice Loop: r23c9=4=r7c9-4-ALS:r7c56|r9c5|r8c4-3-ALS:r12c4-5-r2c7-4-r23c9 => r7c1<>4,r7c2<>4,r9c6<>2,r8c6<>5,r9c6<>5,r6c4<>3,r2c5<>5,r2c9<>5

Naked Single: r6c4 => r6c1<>7,r6c2<>7,r6c5<>7,r6c7<>7,r8c4<>7,r4c5<>7

Hidden Single: r5c7 => r5c7=7,r5c2<>7,r5c3<>7

Two Grouped Strong Links: r46c6=2=r7c6-2-r7c9=2=r4c9~2~ => r4c5<>2

Nice Loop: r2c2=6=r456c2-6-ALS:r1467c1-1-r8c1=1=r8c2~1~r2c2 => r2c2<>1

Hidden Single: r8c2 => r8c2=1,r8c1<>1

ALS xz-rule with A=1 cells: r8c7-4-r78c1|r7c2|r89c3 => r7c9<>2

Hidden Single: r8c7 => r8c7=2,r8c4<>2,r6c7<>2

Hidden Single: r3c4 => r3c4=2,r3c5<>2

Hidden Single: r4c9 => r4c9=2,r4c6<>2

Hidden Single: r4c8 => r4c8=1,r1c8<>1

Two Strong Links: r3c5=5=r3c9-5-r2c7=5=r6c7~5~ => r6c5<>5

ALS xy-rule with B=4 cells: r45789c6-2-r7c12|r89c3-8-r46c12|r5c3 => r5c2<>9

ALS xy-rule with B=1 cells: r2c3457-4-r6c7-5-r5c289 => r2c2<>8

Row Jellyfish Fillet-o-Fish: r3c59|r4c156|r6c1678|r7c1569 => r5c9<>5

Naked Single: r5c9 => r5c2<>3,r5c3<>3,r5c6<>3,r5c8<>3,r1c9<>3,r3c9<>3,r6c8<>3

Locked Column: r46c2 => r2c2<>3,r3c2<>3

Hidden Column Pair: r13c8 => r1c8=39,r3c8=39

Naked Row Pair: r1c48 => r1c1<>9

Locked Column: r13c9 => r7c9<>7

ALS xy-rule with B=1 cells: r4c256-5-r5c6-9-r589c3 => r7c2<>7,r9c2<>7

ALS xy-rule with B=3 cells: r6c12578-9-r589c3-7-r7c1269 => r7c5<>2

ALS xz-rule with A=2 cells: r9c26-2-r7c1259 => r9c8<>4

Three Strong Links: r2c7=4=r6c7-4-r6c8=4=r8c8-4-r8c1=4=r9c2~4~ => r2c2<>4

ALS xz-rule with A=2 cells: r25c2-9-r2389c3 => r5c3<>8

Hidden Single: r5c2 => r5c2=8,r3c2<>8,r9c2<>8

Hidden Single: r5c8 => r5c8=6,r6c8<>6

Naked Row Pair: r6c78 => r6c1<>5,r6c6<>5

ALS xz-rule with A=3 cells: r267c2-2-r45789c6 => r6c6<>3

VWXYZ-wing: r7c1569, r6c6 => r6c1<>9

Naked Single: r6c1 => r6c2<>6,r6c5<>6,r2c1<>6,r4c1<>6,r4c2<>6

Hidden Single: r2c2 => r2c2=6

Hidden Single: r4c5 => r4c5=6

Locked Column: r45c6 => r7c6<>5

VWXYZ-wing: r9c3568, r7c6 => r8c6<>4

ALS xz-rule with A=2 cells: r26c5-2-r9c358 => r2c3<>8

ALS xz-rule with A=2 cells: r25c3-5-r6c56|r5c6 => r2c5<>3

Naked Single: r2c5 => r2c1<>8,r3c5<>8

ALS xz-rule with A=3 cells: r7c269-9-r4c12|r6c2 => r7c1<>5

Two Strong Links: r3c5=5=r3c9-5-r7c9=5=r7c5-5-r3c5 => r9c5<>5

VWXYZ-wing: r7c1269, r9c8 => r9c3<>7

VWXYZ-wing: r5679c6, r9c3 => r5c3<>5

The Solution is completed with naked singles