A revival of Broken Wings

Advanced methods and approaches for solving Sudoku puzzles

Re: A revival of Broken Wings

Postby ronk » Mon Jun 28, 2010 4:33 pm

daj95376 wrote:Previously, I had mentioned a "Dual Kraken X-Wing" configuration and Mike Barker applied it to NoFish1.

I now realize that a (remotely) finned Jellyfish contains both X-Wing patterns.
Code: Select all
 finned Jellyfish c1346\r2378 w/remote fins r5c16,r6c34 => r3c5<>5
 +-----------------------------------+
 |  .  .  .  |  .  .  .  |  .  5  .  |
 |  .  5  .  | *5  5 *5  |  .  .  .  |
 | *5  . *5  |  . -5 *5  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  .  .  |  .  .  .  |  5  .  .  |
 | #5  5  .  |  .  . #5  |  .  .  .  |
 |  .  . #5  | #5  5  .  |  .  .  .  |
 |-----------+-----------+-----------|
 | *5  5  .  | *5  .  .  |  .  .  .  |
 |  .  5 *5  |  .  . *5  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  .  .  5  |
 +-----------------------------------+

If unfinned Jellyfish is true, then r3c5<>5.

If either r5c1|r6c4 is true, then the Jellyfish reduces to finned X-Wing c36\r38 => r3c5<>5.

If either r5c6|r6c3 is true, then the Jellyfish reduces to Sashimi X-Wing c14\r37 => r3c5<>5.

I agree that either the finned x-wing or the sashimi x-wing must be true, but I don't think this means the overall pattern is a jellyfish. Although other cover sets exist, the overall pattern has four base sets (c1346) and eight cover sets (r35678b245). The normal jellyfish would have either four, five or six cover sets.

......Image

Additionally, this example could be considered a poster child for the NoFish class of template eliminations.

Code: Select all
 .  .  . |  .  .  . |  .  5  .
 .  5  . | g5  5 g5 |  .  .  .
g5  . g5 |  . -5 g5 |  .  .  .
---------+----------+----------
 .  .  . |  .  .  . |  5  .  .
*5  5  . |  .  . *5 |  .  .  .
 .  . *5 | *5  5  . |  .  .  .
---------+----------+----------
*5  5  . | *5  .  . |  .  .  .
 .  5 *5 |  .  . *5 |  .  .  .
 .  .  . |  .  .  . |  .  .  5

If all the guardians r2c46 and r3c136 -- marked (g) -- were false, there would be an impossible jellyfish in c1346. Therefore, at least one of the guardians must be true and r3c5<>5, since it sees all the guardians.

Perhaps the subject of allowing fish to have remote fins should be revisited. Obi-Wahn didn't allow them, my generalized-fish-finder (GFF) doesn't use them and, the last I heard, your GFF didn't use them either.
ronk
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Posts: 4764
Joined: 02 November 2005
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NoFish 022 - 563 List

Postby tarek » Sat Jul 03, 2010 10:51 am

This is the NoFish list that I originally posted on the old forum. It Follows Obi-Wahn's 21 puzzles posted in his original NoFish List.

The puzzles solution path will start at the NoFish move. These eliminations were verified through template eliminations. Thanks to Danny & blue for re-verifyiny the eliminations with corrections.

Thanks for ronk & ttt for saving a copy that helped bringing this back.

[EDIT: List corrections updated]

Nofish022-563: Show
........9..5..1.3..7..6.4..6....3..2..4.8..1..3...75....9..5.6..1..3.7.....2....8 # NoFish022 r1c1<>2
..7..2..1.5...3...9...4..8..2..7.3....1.....54..6........3..2....8....4.6...5...9 # NoFish023 r56c2<>3
........1.....2.6.....5.8..2..7....3..8..1.4.16..9......1..85...9..6..2.4..3....7 # NoFish024 r1c1<>3
........7....38.9...46..5....5.......8...1.3.9...7...6..6.....4.7..8..1.3....52.. # NoFish025 r4c7<>4
........3.91.2..6.8....71....2..6.7....1......5..8.9....73....4.1..5..8.6.....2.. # NoFish026 r5c3<>3
.....1..2..3.6.....8.5...7...7....8..6.9..3..5...4...1.1..7.4....98...6.2....3... # NoFish027 r6c6<>2
..2..3..5.1..4..9.6..7..8....3.......5.2..4..8....6.....7.1.3...9...5.6.4.......8 # NoFish028 r4c4<>8
..8.....6.9.....2.5....37.....7..9...1..8..5...2..6..4..45....3.7.....1.6....98.. # NoFish029 r2c5<>1
........9..5....3..7...26.....65.1..8...4.........3.7...19..4...6...5.2.3...7...8 # NoFish030 r1c5<>8
........4..8..3.5.2...7.1....6....8.5.......3.1.4..9....7.1...6.3.8..24.9....5... # NoFish031 r45c2<>4
.....3..4.1..8......7.1..6..2......1..39..8..6....5.7.....4..2...8..75..9..6....3 # NoFish032 r7c7<>1
.....7..6..1....3..9..5.2...8...91...14.3....5..2....7..6...9...2.....5.3....8..4 # NoFish033 r9c4<>7
.....1....9..8...26..5...3...27..6...1...3.8.4.......9......7....8.6...134...9.5. # NoFish034 r1c5<>7
.....5..7..4....6..9..8.2.............8.7.4.12..3.......7.4...9.3.2...5.6....18.. # NoFish035 r2c1<>3
8..6..1...2...7.....9.4..3.1.........3..25.8....9......5..8..........91...4..3..2 # NoFish036 r5c4,r6c9<>1
......1..8..7...3..5..6...26....1....3..5.9....42..7...7.9.......2.3.5..1....4.8. # NoFish037 r3c6<>8
......3..2...8.1...5...9....8..1.9....67...3.4....5..2..3.2....1....47...9.6...8. # NoFish038 r8c4<>3
......7...2.1...3...9.5..8...89......7...45..3......1.6....84...1..7..9...53....2 # NoFish039 r4c1<>4
......9..5..4..73..6..7...23...6....21.9..5....4....8..2.8.......7.5.4..9....3.1. # NoFish040 r7c6<>6
......9..5..8...3.....41..2..6.9....1.....7...2...3.8...8..2...34.6..5...9..7..1. # NoFish041 r5c8<>5
......9..7..6...3..1..8...2.3..9....8.41..7..5....4.8...2.4....6....35...8.7...1. # NoFish042 r1c5<>2
.....3....4.7.....6...8.1....5..2....7.4..9..8...1..3......5....6..9..8.1..6..7.2 # NoFish043 r1c9<>5
.....4...3...5.9...6.8..12.....1.....2.7...3...9..678...89.....4...2.5...7...3.1. # NoFish044 r1c1<>5
.....5...7..2..1...8.39..2.1..8.......6.7.9...4.....3...2.6.....3.1..7..9....4.8. # NoFish045 r6c9<>6
.....79....48...3..6..1...21..2........56.7...9.....8...7......8..9..5..23...4.1. # NoFish046 r6c9<>6
.....81..4..3..9...5..7..2.8..4.......1..57...2.....3...3.8....9..6..5...7...1.8. # NoFish047 r8c9<>4
.....9...6..2......3..5.8..35..4......83..1..9....7.2..........2....19..84.6...3. # NoFish048 r1c9<>5
....1.......5..9...8...4.3.5...3.7...9.4.6.8...4.....2.3.8...1...6..75..2...9.... # NoFish049 r1c3<>2
....4....6..9..1...3...7.2...8.5....7..4.29...5.....3.4....5....2.3..7....9.6..8. # NoFish050 r1c9<>8
....5....7..6...3..8..3.1..3...92....4....9....51...8.17.3.......6.4.7.......9..2 # NoFish051 r1c1<>2
...1..7..9...6..8..5...3..22.34..5.........1..7..8...3..8..7....6.2..4..1......9. # NoFish052 r5c5<>9
...1..9..6......3..1...8.....5.6.7...9.....8.3....4..2..4..3...2...9.5...8.7...1. # NoFish053 r5c79<>1
...2.....3...8......4..71...6..9....8..4...3...1..5..22..6..3...7...89....5.1..8. # NoFish054 r3c4<>3
...2.....6...1..3..5...79..1...4.7....9....8..3......2..732....4.....5...8...9.1. # NoFish055 r4c3<>2
...2..8..5...6..3..9...1....1..7.9....3..5.8.6....4..2.2..3......4..97.....8...1. # NoFish056 r7c3<>8
...2..9..1...8..3..47..5.....49..7..5.6..1.8.........26....4....8....5....2.3..1. # NoFish057 r8c9<>9
...2..9..5....87...4..9..3..7..1......34..58...6.....2..2.6.....8...34..9......1. # NoFish058 r1c6<>6
...2..9..7...5..3..4...1.....1.6.7...3.....8.9....4..2..4..7....2..9.5..3..8...1. # NoFish059 r45c9<>4
...2..9..8...1..3..6...4.....3.4.7...1.....8.4....6..22....3.....7.8.5....49...1. # NoFish060 r5c9<>6
...3..9..5......8..7..64..28..........2..17...4..9...3..6.7....3..4..5...9...2.1. # NoFish061 r4c8<>5
...4.....9.....1...78.5..3....9.....6...1...2.3...8....1..2..8.2....79....43..... # NoFish062 r4c9<>4
...4..1..6...5..3..7...89....47......8..9....1...4...25....2....3..6.7....91...8. # NoFish063 r3c1<>2
...4..7..1...5..8..3...9..2...87.5...6.....1......2..3..2......8...6.4..75.1...9. # NoFish064 r5c3<>3
...4..9..7....538.....3...2.9.1.......4..27..6...8...3..5.9....8....7....3.6...1. # NoFish065 r1c2<>1
...5......8...49....7.1..3.....3....1.42.87...9......2.4..6.5....29...8.3....7.1. # NoFish066 r1c12<>2
...5.....2.9..8.3..7..2.1...3.6.......4..59......1...25...9.....6...47....13...8. # NoFish067 r7c78<>2
...5..7.......8.3..1..6....4..7...8..3...251...6..9..2..83......7..2.1..5....4.9. # NoFish068 r12c5<>1
...5..9..1....4.8..7..6...29...8......4...7...5...2..3..8.9.....2.3..5..6....7.1. # NoFish069 r4c6<>1
...6.....8...5.9...7...1.3.4...3.....5.9.478...1.....2...2......6..8.5..9....7.1. # NoFish070 r1c3<>2
...6..1..5......3..84...9...3.......9....57....1.8...2.6.9.......7..45..2...3..8. # NoFish071 r4c9<>6
...6..9..2...4..3..7...5....5..3.7....9....8.4....1..2..8.9.....6..125.....7...1. # NoFish072 r1c9<>8
...7.....1.7.5..3..8...29..6...3.7....91...8......4..2..3.8....4..9..5...7...6.1. # NoFish073 r9c7<>2
...7.....2...1.9...5...4.3..8.6.....3...9.78...1.....2.6.2.......9..35..7...8..1. # NoFish074 r1c3<>6
...7..23.8...1.....4...9...7...5.9....63...8..1......2.9..4......56..7..3....8.1. # NoFish075 r6c6<>4
...7..9....5.1.....6...4.8.4..3.......1.487..8...9...2.9.6...1.7...2.5....8.....3 # NoFish076 r1c8<>6
...7..9...86.4.........5.3..6..1......3..97..49.2...8..7.3.........6.51......8..2 # NoFish077 r7c9<>6
...7..9..1....5.8..3..4...2...2.......6...7...4..8...3..7.9.....2.4..5..86.....1. # NoFish078 r4c6<>1
...7..9..1...2..3..4...8.....9.1.7..5...6..8.6..3....2.3...4.....2...5..7..9...1. # NoFish079 r5c9<>4
...8..1..6...9..3...2..4.......6.7...9.5...8...4..1..2...3..5...8..2..1.4....7.9. # NoFish080 r12c9<>4
...9..1...2...5.....7.3..8.8..........6..49.....1....2.9..6.7..5..2...1...4..8..3 # NoFish081 r5c1<>1
...9..1..6.7....3..4..2......5.1.....8...59..3....7..2..2..4...1...3.7...6.5...8. # NoFish082 r9c9<>9
..1...7...6.3...8.....4...23....7....8.9..5....56...1...28......7..1..9.4....5..3 # NoFish083 r8c9<>4
..1...9...5.6...8.3....4..2..9......8..9.3.......5.7..6..4....3.2...9.1...7.8.5.. # NoFish084 r1c2<>7
..12.....5...7.9...4.....3.6..1..........938...8.5...29..4......2....7....6..3.1. # NoFish085 r7c2<>3
..13..9..5..6...3..7..4...2.....1...6..85.7....29...8...92......4....5..8......1. # NoFish086 r9c9<>4
..16.........4.9...2...5.8..5..3.7..3......1...89....2.9.7.......4..15..6...8...3 # NoFish087 r2c8<>3
..16.....2.....9...8...7.3..4....3..9....5.8...7.4...2..64......3...87......2.51. # NoFish088 r6c6<>6
..18.....7......3..2..5.9..5...4......3...78..6...1..2.9..2......56..8..4....7.1. # NoFish089 r23c3<>8
..2......3..4......7....12.4..1......6...59....8.7..3.2..6......5..1.7....9..3.8. # NoFish090 r7c3<>4
..2......5..9..8...6..37.....84..3...9....1..3.6.5..2..7...2.....4.8.9.....6...3. # NoFish091 r2c9<>7
..26.....7...5..3......19..5..3..7...9....18...6.4...2..39.....4...2.....8...7.1. # NoFish092 r12c2<>1
..27.....8...3.....3...91..7..6..9.......5.3...4.8...2.1.3.......6.4.7.......1.8. # NoFish093 r5c9<>1
..29.....7...3.....8....1..9..4......5....83...1.7...2..42.....3...5.9...6...1.8. # NoFish094 r12c6<>8
..29.....8....51...7..4..3.1..46.....4...89.....7....2..5......9...1.7...6...3.8. # NoFish095 r7c4<>2
..3......9..6..1...5..7..2...4..5...5...1.9...7.2...3...1..4...2..9..7...6..3..8. # NoFish096 r1c9<>4
..3.5....7..8...2..9....1..1..4.......82..9...4...7.3...5.4.....6.3..7..2....9.8. # NoFish097 r5c9<>5
..32.....8......3..9..7.1..4..5.......2..89......1...2..6.3....5..4..7...1...9.8. # NoFish098 r7c6<>2
..34.....2.....9...7..1..8..6...5...9...7.1....83....2.4.6.......5..27......8..13 # NoFish099 r1c1<>1
..37..9..1......8..5..4...28..........96..7...6.2....3..4.6.....2.8..5..7....9.1. # NoFish100 r4c6<>1
..4..5...7..9..1...8..3..2...68......2..1.9..1...7..3...5..4....9..2.7.........8. # NoFish101 r9c9<>5
..42.5...9......3..7..8.1..8...6......5...9.....7....2..6.2....1..9..7...3...4.8. # NoFish102 r4c3<>2
..46.....8.....9...2....73...1..3...9...5..8..7..4...26....8....5.9..2....3.7..1. # NoFish103 r2c4<>2
..49..7......5..8..1...6..2...6..5...7.28..1.9.......3..3.......6..2.4..8..1...9. # NoFish104 r3c1<>3
..49..7..1...3..8.....65..27.....5....92...1......6..3..3.7.....6....4..8....1.9. # NoFish105 r79c9<>6
..5......9..4...2..8..971..1...2.....7.6..9....4....3..6.1.......3.5.7..2....3.8. # NoFish106 r1c79<>3
..5..49..7..6...3..1..3...24.............97...2.1...8..6....2....83..5..9....7.1. # NoFish107 r45c5<>2
..51.....8...6..3..4...79..9.....7....2.3..8......5..2..7.2....3..8..5...6...4.1. # NoFish108 r1c6<>2
..52.....1...8..3..7...49......5.7...4.....8...9..1..2..87.....3...9.5...6..3..1. # NoFish109 r5c3<>2
..54.....8...1..3..7...29..1...5.7...6..2..8....3....22..6......3..9.5....4..8.1. # NoFish110 r7c9<>4
..57.....4...8.1...6..5..3...7.1.......3..9...8...5..2..9..2....5.6..7..3...4..8. # NoFish111 r5c3<>2
..6...8..1..7...3..9..4...2.4.3.....7...2.9....5....8.2..9......3...57....8.6..1. # NoFish112 r7c6<>8
..6.7....9..4..1...8.3...2.7..6.......5..8....1....93...2.5.....3.1..7..4....9.8. # NoFish113 r4c6,r6c9<>5
..61..7...9...4.8.3.......2.4...........3.5..2....8.1.8.......3.7.5..89...1..64.. # NoFish114 r4c5<>2
..63..9..1......8..7..5...2..5.2.....9.4..7..4.......3..2..8...8...7.5...3.9...1. # NoFish115 r6c7<>8
..64.....8...1..3..5...29....4.5.7.....6...8.1.......2....94...2.....5...3.8...1. # NoFish116 r5c9<>4
..7..9...3..4......1..2.8....8.......9..3.1..4...5..2...5..7...2...1.9...6.5...3. # NoFish117 r2c9<>7
..7.4.9..6..1...3..5......2..89.....3...2.....9.7...8..2...5.....43..7..8...6..1. # NoFish118 r6c9<>5
..74.....2......3..8..5.1..1...7......46..9...3......2..9.4....6..1..7...5...2.8. # NoFish119 r4c9<>4
..74.....8.....9...2..5..3.3..9......1...738...4.....2..52......9..3.7..6....8.1. # NoFish120 r7c5<>4
..76.....8...1..3..5....9..1...4.7....653..8..9......2..3.7....4..8..5...2.....1. # NoFish121 r9c9<>9
..78.........2..3..9...51..5..6..9....1..7.8.....4...2.6..1......89..3..4....37.. # NoFish122 r1c2<>2
..79.....6...2..3..1...58..4..7..9.........8...3.1...2.8.4.......9...7..2....3.1. # NoFish123 r8c6<>8
..8......3..7..1..69..5..2..5..2.......1..9..4....8.3.1...4.....3...9.....23..78. # NoFish124 r5c9<>7
..8......6......2..7.23.1...1...7.....5.2.9.....4..83...3.5.7..9....13...4.....8. # NoFish125 r1c6<>5
..8...1..7......3..9..5...2.1...8.....249....6....19...5..1......4..27..3..6...8. # NoFish126 r4c9<>5
..8...9..6......3..4..7...2.5...4...1....67....39...8..2.4......17..85..9......1. # NoFish127 r12c9<>4
..82.....1...5.9...7...4.3...2.3.7.....6...8.9....1..2.....9....6..7.5..3..8...1. # NoFish128 r7c5<>2
..82.....5.....1...6..9..3.1..4........78.9...7...1..2..2.5.....9.6..7.......3.8. # NoFish129 r9c9<>1
..84.....5...1..3..2...79...1..5.7....4....8.9.......2..6.4....3....25...7.8...1. # NoFish130 r4c9<>4
..86.....9......3..4..5.1..1.3.4.....5.8..9.......7..2..2..3.......1.7..7..9...8. # NoFish131 r1c6<>2
..9......3..7...2..5..4.1...6..8......7..19.....2...3...2.6.7...4...95..1......8. # NoFish132 r1c4<>3
..9..5...8......2..4..6.1...1..24...7.....9....5..8.3..3.4.......2..97..6......8. # NoFish133 r12c9<>4
..9.7....8..6..1...4...592..7.8.....1....4.....6....3.5..9......2...17....3....8. # NoFish134 r7c5<>3
..94..7......3..8..6...1..2....7.5...2.9...1.4..1.6..3..6.......7..8.4..3..5...9. # NoFish135 r45c9<>6
..96..7..6...5..8..3...4..2...7.35...4.....1.2.......3..5.......7..6.4..8..1...9. # NoFish136 r7c1<>3
..98..1..5......3..8..7......7.5.....3.4..9..6....1..2..4..9...1...3.7...6.2...8. # NoFish137 r5c9<>8
.1.4.....5...2.7....9....8..4..3......6..95..8..7...1..3....4......1...2.....2.93 # NoFish138 r1c6<>3
.3...89..5......3..4..6...2.9.1.........527..3....4.8...6......2....95...8.7...1. # NoFish139 r5c9<>6
.3..5....1......2..469..8...9.6.......4.3....8....21....5.4.9.......87.....1...3. # NoFish140 r5c9<>5
.4.9.......2.3.........71..7...4.9...64....3...5..1..26.92......3..6.7.......5.8. # NoFish141 r9c9<>1
.5..1......63..........92...1.4.......3.5.8.......7.2...46.....7....21...9..8..3. # NoFish142 r79c1<>2
.5.6..1........38.7...4...2.1..7....2..8..9....4..5..3.6.9.......3..2...8...1.7.. # NoFish143 r79c6<>3
.5.9.........2.7....4..8.3.9..6..5...3...4.8.....1...2.8.7..41...6.3....1....5.9. # NoFish144 r1c3<>2
.5.9.........8......7..21..6......3...84..9...1...7..2.841..7...9..3....2....5.8. # NoFish145 r2c9<>3
.6.1.........5..3.8....49..21....7......3..8...5..9..24..8......9...6.....7...51. # NoFish146 r9c9<>3
.6.4.......1..38......9..2...8.1.....5.6.....2....73...4..8......92..1.......593. # NoFish147 r13c1<>3
.6.5..1....9.8.........2.3..2..6.9....61..7....5..4.8..4.9.....8...7.5....1..3..2 # NoFish148 r7c1<>3
.7....9....64...3.5....1..2......7..4..3...8...2..8.1..952.......1.9....3...5.8.. # NoFish149 r4c89,r9c9<>9
.7....9..1..5...3..8..6...29..........63..7...5...2.8...4.9....2....85...3...4.1. # NoFish150 r4c9<>6
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6.7.2.....8....9.....4...3.5...9.....2.1.......3..87..9..3...8..6..5..1...1.....2 # NoFish444 r2c6<>7
62.5.........6..8.......9...3....7....548..1.4....9..2..7.2....9....45...6.1....3 # NoFish445 r7c6<>8
7..........4.8.9...2.5...3...6.3.....8...9......2..7....9..4.8..3..6.51.1.......2 # NoFish446 r2c4<>7
7.........2.9.......8.4.1..5.3..1......7..9...6..8..3...41..7...3.6...8......5..2 # NoFish447 r1c9<>5
7.........3.29......9..51...4.1.........6.9..2....8.3...5...7...6...4.8.1..3....2 # NoFish448 r7c8,r7c9<>9
7.........5.2..9....1.8..3.4...9.....2...1.....6.2.78...96..5...8.....1.3....4..2 # NoFish449 r1c4<>4
7.........8.5..9....6.81.3..3..9....6..2..7....1..4.8.......5...9...2.1...4.3...2 # NoFish450 r7c9<>7
7.....9.....6.......1..2.3..9.3.......5.817..2...4..8..6.7..5.......4.1...4.9...2 # NoFish451 r8c9<>6
7.....9....65...8..4..3...2.9...4.....12..7..5......1...8.6.....3...15..2..7....3 # NoFish452 r4c4<>3
7.....9...3.6...8...1..5..2..51......2...4...6...8.7..4..3..5...8...2.1...9.....3 # NoFish453 r7c5<>7
7....4....8.1...3...5.2.9..1..4......6....7....2..9.8....6..5..4...8..1..9...7..2 # NoFish454 r7c9<>4
7....81...6.....3...954.....5.......8...1.9....2..47..4..9..5...3.....8...1.7...2 # NoFish455 r9c4<>3
7...1.....8.2..9.........3...3.......6..5.7..1..4.9.8...5..73...4..8..1.9..6....2 # NoFish456 r5c6<>3
7...2......15..9...4...8.3..5.9..7.............6..3.8..9.6...1...8..75..3...4...2 # NoFish457 r5c1<>2
7...2......8...1...9.1...3..6.47.........59..4..3...8..3...4.1...56..7......8...2 # NoFish458 r4c1<>2
7...2.....3....9....8.1..3..6..3.......4..7....1..5.8...46..3...9...8.1.5...7...2 # NoFish459 r4c1<>2
7...2.9...5.6.......8..1.3..9.........34..7..2..15..8..6....5.......841...4.....2 # NoFish460 r4c5<>6
7...4.....6.2...3...1...9....9......5..1..7...2...9.8......75..3..4...1..8..6...2 # NoFish461 r7c8,r7c9<>9
7...4.....9.....3...29..1...3..8....6....5......7..92..4.3..7....5..1.8.9...6...2 # NoFish462 r1c6<>6
7...4.9.....5...8..6..8...2.5.9.....3...2.7.......8.1...91......4...75..2...6...3 # NoFish463 r4c3<>1
7...5......39..1...9.8...2..2..4......5...9..6..7...3..4.3.1.8...1..27......9.... # NoFish464 r5c8,r5c9<>1
7...6.....8...5.3...92..1...4.1.....2....8.....1..49....6...7..5....9.8..3..4...2 # NoFish465 r7c8,r7c9<>1
7...6.9...8.5.......2..4.3..6..9.........17....52...8..4.7..5.......8.1...6.3...2 # NoFish466 r2c9,r3c9<>6
7..1......5..3.9....6.4..8....8.......1.5.7..3.......2..8.7.5...4...9.1....2....3 # NoFish467 r4c1<>2
7..1......6....9....3.5..8.1.47.5....5..3......8..4..2..98..7......7..1.2....6..3 # NoFish468 r1c6<>2
7..2.......5..91...6..3..8.4....5.....61..9......73..2.2..8......1...7..9....4..3 # NoFish469 r4c2<>8
7..2......3...19....5.6..8....5......89.3.7..1....4..2..4...5...6..8..1....7....3 # NoFish470 r9c6<>2
7..2..9....4.1.....5.....3...25......3.....8.1...3.7...8.....1....64.5....9..7..2 # NoFish471 r3c9<>8
7..2..9...4...5.....1.8..3...4..1....2.3...8.....9.7...5..6.......7...1...3..4..2 # NoFish472 r7c9,r8c9<>4
7..2..9...4...8.....6.5..3..9............47.....1...8..3..9.5..8..6...1...4..7..2 # NoFish473 r4c9,r6c9<>4
7..3..........41....5.2..8..6...7.....85..9..3...1...2..4.8.7...2...65..9.......3 # NoFish474 r2c8<>6
7..3......2....9....4.1..8.5...8......34..7...1......2..8.5.....9.7...1.6....9..3 # NoFish475 r6c8<>9
7..3......5..4.9....1..8.....3.6.....4...9.8....1..7.2...2..5...89.7..1.6.......3 # NoFish476 r1c7<>2
7..3..1...8..2.........5.....4.......1..6..3....8.79...6.1..7..3...9..8...5..4..2 # NoFish477 r3c9<>4
7..4..9...5...1.....3.2..8....3......6...5.1.....74..2.4..6.7..1......9...2..8..3 # NoFish478 r4c1,r5c1<>9
7..5.........1..8.....389....6.9.7..8......1..5.4....24.........9.2..5....1.7...3 # NoFish479 r7c2,r7c3<>8
7..5.......1.3..8..8...49..3...9.7...5.....1...4..6..2.9.8.......2.1.5..6.......3 # NoFish480 r5c5,r5c6<>8
7..5......3.....8...1.4.9...6.......2.....7..5.3.1...2.8.6..5....4....1.9...2...3 # NoFish481 r1c6<>2
7..5......3..6.9....1.3..8.4....1....5.9..7......8...2..6...5...9..7..1.8....4..3 # NoFish482 r5c9<>4
7..5......5..2.1....6..89...8...4.....9.6.7..2......3...49..5..3...7..8.........2 # NoFish483 r9c4<>3
7..5......6..3.9....5....8..4...9...1...8.7....3.....2..86..5..2....4.1..9..7...3 # NoFish484 r6c8<>5
7..5..9...4...8.....6.1..3..3...4.......2.7.....9...8..8..7.5.....6...1.4.9..3..2 # NoFish485 r5c9,r6c9<>4
7..6.......2...9...3...4.8.1....3.....5...7.....9.7..2.9.2...1...6...5..4....8..3 # NoFish486 r2c8<>5
7..6.....1...8..3..5...12.....5..9..3....478...6.....2..93.....4.....5...8..7..1. # NoFish487 r7c5<>6
7..6..1...3...8.....2.9......6.4.....8.2...3.5....79......127.....3...8...4..5..2 # NoFish488 r3c9<>4
7..6..9...1.2...3.....5......2..4....3....7..5...9..8..6...75....4.8..1.9..3....2 # NoFish489 r7c9<>4
7..8..........5.8..9..241...6.......5...1.9....3..7..2.8.9.......1..67..2...4...3 # NoFish490 r4c1,r4c3<>8
7..8......4...19....2.5..3..9.........5..47.........8.3...2.5....86...1......7.92 # NoFish491 r6c6<>9
7..8......5..2......1..49..3...5.7.....1...8...6..9..22.87..5...9.....1......6..3 # NoFish492 r3c9<>6
7..8......5..2......3..19...4..5.......3...8.9....7..2.8..4.7....6..9.1.2..1....3 # NoFish493 r2c7<>4
7..8......6..2......4..39..1....7.....3....8..5.1....2..8.4.7..9......1..2...5..3 # NoFish494 r1c7,r1c9<>1
7..9.......6....3..5..4.1...3.17......8..59..1.......22...6.....4...17....93...8. # NoFish495 r1c5<>2
7..9......5...3.8.....4.2..6....7....4.8..9....3....12.9.6.......8.2....1....5..3 # NoFish496 r7c3,r9c3<>2
7..9..1......5....8...17.3...6..2....7..4..8.3..1..9...9.6.....5...8......1..3..2 # NoFish497 r2c3<>2
7.94..1.......32...6..5..8..1.6.......5.7.9..8.......2..4.8.........97..2..1....3 # NoFish498 r7c6<>2
8.........1.6..9....4.5..3.29.8.........3.7.......1.8...6.4.8...3...7.1.5..9....2 # NoFish499 r1c4<>2
8.........7.6..1....9.4..3..5...8...1...7.9....43...2....1.....3....278..6...5..2 # NoFish500 r1c3<>5
8.....1...2.6.......9.3.....4.9.......5..72....7.8..3....14.9...3...5.8.6.......2 # NoFish501 r1c9<>6
8.....9...1.2...3...5....8..4.........7.938..3....5.1.....3.7...6...1.9...9.....2 # NoFish502 r7c2<>2
8.....9...1.5...3...4.2.......9.2....5....7..3...1..8...9..35...6..4..1.7..8....2 # NoFish503 r8c3<>2
8.....9...1.64......7..3...9...6.....3...1.8...57....2...8..7...6...5.1...4.....3 # NoFish504 r7c5<>9
8.....9...5.1.....2.7..3...1.....7...3.9...8...6.4...2...8..5.......7.1...4.6...3 # NoFish505 r1c9<>4
8.....9...7..3......15...8.5...8..1...39..7...4......2.2...45..9...1......6.....3 # NoFish506 r8c4,r8c6<>8
8.....9...7.4.......5.2.83..4.........3..97..2..67..8.9...3.5.......7.1...6.....2 # NoFish507 r9c1<>4
8....1....6.5..9....794..3.....2......56..7...1.....8...3...5...4.8...1.9..7....2 # NoFish508 r7c1<>2
8....3....9.2.......4.5.1....6.......2.1.79..7...8..3.5.....7...6..4..8...39....2 # NoFish509 r1c8,r1c9<>7
8....3....9.6.......2.5.1...4..8.......7..9..9.1....3..5.1..7....3..5.8.6...4...2 # NoFish510 r2c9<>7
8....7....2....1....94...3..7.6.....3.....8....5.2.9....63.....4....9.8..1..5...2 # NoFish511 r2c6,r3c6<>8
8....9....4.7.........2.1..7..4......2..879....5..1.3.1.........9..3..8...3..5..2 # NoFish512 r3c9<>3
8...1.....172..9...5...7.3..2...........4.7.......3.8..3.7...1...6..85..4...9...2 # NoFish513 r6c9<>4
8...2.....1.7..8....79...3..3..7......41..9..6....5.8..9...47....56...1.....3...2 # NoFish514 r4c1<>2
8...2.....4.1...3...5...9....745....2.....7....3..9.8...68..5..7......1..9..4...2 # NoFish515 r1c9,r3c9<>4
8...2.....6.7..9....1..5.3.....1......9..37..4..6...8..7.8.......5..4.1.....9...2 # NoFish516 r4c1<>2
8...2.....6.7..9....5..1.3.....4......9..57..1..3...8..7.6..5....3..9.1.........2 # NoFish517 r4c1<>2
8...4.....7.9...3...92..1....2.1....6....3....5.8..9...4...57....3....8.....6...2 # NoFish518 r4c9<>6
8...5.....4.....3...27..1....1.3.....7.8.....5....29...6...97....31...8.4..5....2 # NoFish519 r4c9,r5c9<>5
8...5.....4.7..9....1..4.3......23...6..1.7..4..9...8.9.....5......6..1...38....2 # NoFish520 r7c6,r8c6<>3
8...5.....9....1....64...3.5....8.....7.1.....2....9....3.9.7...4.6...8.1....5..2 # NoFish521 r5c9,r6c9<>5
8...7.....7.2.......3..51...2..1......6...9..4..8...3...93..7..5....4.8....56...2 # NoFish522 r3c8<>9
8..1.......6.5.9...7..64.3.61....7.......2.....53...8..9.....1...4.8.5.......7..2 # NoFish523 r7c1<>2
8..2......7....9....1.3..8.4....9....5.1..7....3.6...2..9...5..6...8..1..2...4..3 # NoFish524 r4c4<>8
8..2.....4...7..3......59....6...7...1.....8.5..43...27....4....2..6.5....38...1. # NoFish525 r1c9,r3c9<>4
8..3......9...21....7.4.....5..7......6..19...1.....3.3...9.7....46...8......5..2 # NoFish526 r9c8<>1
8..3..7...4..9......1....8.3...8..1...9.6.5...7...4..2.5....4..2......9...6..1..3 # NoFish527 r8c4,r8c6<>8
8..4........67.1....6..5.3..1..2......5...9..7..3...8.4..8..7....9.14...........2 # NoFish528 r1c2<>2
8..4......1..73.....7...9....9.1....6..7...8..3...5..2.....47...5.....1.4...2...3 # NoFish529 r7c5<>9
8..4..1....2.9.........7.3..3...2.....76..9..1...4..8..9.1.........3.8....6..5..2 # NoFish530 r3c5<>8
8..4..7......5..1...3...9.2...58......1..3....2......3..6.2.5...4.1...9.7.......8 # NoFish531 r9c2<>3
8..5..9...6..2......7....3..5.........1..37..4..6...8..2..8.5......4..1...9.....2 # NoFish532 r4c4,r4c6<>2
8..9........5...3...5.7.1..6....2....4....9..7.3.5..8...73.....9...4.....1...8..2 # NoFish533 r2c7<>2
8..9......6...7.2...5.3.1..3...8......75..9...4......2.2....7....14...8.9....5..3 # NoFish534 r8c6<>2
8..9..1....6..4....7.....3..8..1.7...6.2...8...5....1..3..7..9....6..5....4..8..2 # NoFish535 r1c9<>4
8.4.2.....7....9....5....3..6.........19..7.......4.8..1...75....96...1.3...8...2 # NoFish536 r4c1<>2
81.7..9......6......5....8.3......1...9..47...6..5...2.7.9..5..2...8......4..1..3 # NoFish537 r4c4,r4c6<>8
9..........68..1...5..2..3..7..5......3..19..4..6...8...7.4.....1...97........8.2 # NoFish538 r3c1<>8
9.........7.1.3.....8.2.1..4....5.......1.9....27...3..5.9..7....6....8.3....4..2 # NoFish539 r1c9<>4
9.....1....5..8.3..4..7.....3..25.....6...9..7..1...8..1..6.....28..47.....3....2 # NoFish540 r3c4,r3c6<>2
9.....1...4..8..3.6..7....2..5..2...8...1.......6..9....9..5....2.3...8.1...4.7.3 # NoFish541 r5c6<>9
9.....2...7.8...3...5.1....1..34.....6....9.......2.8...46..7...8..9..1.3....5..2 # NoFish542 r5c1<>2
9.....7...1.3...8...6.4...2..89.....3.....5...2..6..1.5....8....7.2...9...4.1...3 # NoFish543 r1c6<>5
9.....7...5..1..8...43....2...2.......6.4.5..8....9.1.2....64...7..5..9...1.....3 # NoFish544 r4c3<>3
9....2....3.8.......7.4.1...4.......6....59....27...3..1.6..7....5..9.8.4...3...2 # NoFish545 r1c9,r2c9<>4
9....47.....5...8...1.3...2.6.2..........75..3...8..1...5...4..2....1.9..7.6....3 # NoFish546 r2c9<>6
9....5..........3..7..8.1...1..7....4..3..9....32...8...51......6...97..8...4...2 # NoFish547 r7c7,r7c9<>3
9....5....6.3..7....4.1..8.2.............95...7.4...12..1...4...8.67..9......2..3 # NoFish548 r1c4,r1c5<>2
9...2.7...4.....8...5.3...2..........7..425..6..9...1...3...4..8...5..9..1.7....3 # NoFish549 r4c4,r4c6<>3
9...4.....8...71....62...3...2..5...7.........1.8..9.......97...5.3...8.4...1...2 # NoFish550 r5c9<>4
9...4.1...3.6.......7..8....54..29.....1.......8.7..3..6.5..7.......9.8...1.3.5.2 # NoFish551 r1c9<>6
9..2.......3....8.....5.1..5..4.......7..39...1.6....2..5.8....4..9..7...6...1..3 # NoFish552 r1c8<>5
9..2......4..5.7....3..1.8....8..5..2...9..1...4.....2..85..4...1...6.9.....7...3 # NoFish553 r9c6<>2
9..2.....5.....1...3..9..8...4..5....1.6..9..8...7...2..9..4....6..1.7..2..8....3 # NoFish554 r2c8<>4
9..2..1...6...5.....7.8..3.1.2.7.....4.......8..1..9...3..9.7.....6...8...5..4..2 # NoFish555 r8c9<>1
9..2..1...6...5...5...7..3...7..4...2...........58.9...1..6.7.....9...8...4..3..2 # NoFish556 r6c9<>4
9..4.......3...1...6..7..8...5.41....4.6..9..7...8...2..1..5....2..9.7..8.......3 # NoFish557 r2c8<>5
9..5.......6....8..7..3.1..35...........7.9....4..8..2..54.....2....17...8..9...3 # NoFish558 r3c8<>5
9..5......1..4.7....3..6.8.4..9..5....8....1..7..3...2.2....4.....7...9.6....1..3 # NoFish559 r8c6<>8
9..6..........538..7..4.1.............5..39...8.57...21...8.....6.9..7....42....3 # NoFish560 r4c3,r6c3<>3
9..6......7..8.1....2..9.3...37......1..4....8....29...4.3..7....6.1..8......5..2 # NoFish561 r9c8<>9
9..7..........18....6.2..3.3...4.9...7...5.8...16....2.2..9.7....53..........8.1. # NoFish562 r8c2<>8
9..7..8...1..2......5..4.3.3......8...6.9.7...8.2...1..4.1..5......6..9...7.....2 # NoFish563 r8c2<>2
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tarek
 
Posts: 2610
Joined: 05 January 2006

Re: A revival of Broken Wings

Postby daj95376 » Tue Feb 25, 2014 1:08 am

To make a long story short, my search for Kraken fish examples of Broken Wings took an interesting turn when I discovered an old post of mine and I updated the logic a bit.

Code: Select all
 unfinned Jellyfish r1245/c1279         (exemplar)
 -- eliminations legitimate
 +-----------------------------------------------+
 |   X   X   /   |   /   /   /   |   X   /   X   |
 |   X   X   /   |   /   /   /   |   X   /   X   |
 |   *   *   .   |   .   .   .   |   *   .   *   |
 |---------------+---------------+---------------|
 |   X   X   /   |   /   /   /   |   X   /   X   |
 |   X   X   /   |   /   /   /   |   X   /   X   |
 |   *   *   .   |   .   .   .   |   *   .   *   |
 |---------------+---------------+---------------|
 |   *   *   .   |   .   .   .   |   *   .   *   |
 |   *   *   .   |   .   .   .   |   *   .   *   |
 |   *   *   .   |   .   .   .   |   *   .   *   |
 +-----------------------------------------------+

Code: Select all
 unfinned Jellyfish r1245/c1279 and "~" cells empty in candidate grid
 -- Broken Wing pattern
 -- eliminations can not all be false
 +-----------------------------------------------+
 |   ~   X   /   |   /   /   /   |   ~   /   X   |
 |   X   ~   /   |   /   /   /   |   X   /   ~   |
 |   *   *   .   |   .   .   .   |   *   .   *   |
 |---------------+---------------+---------------|
 |   X   ~   /   |   /   /   /   |   ~   /   X   |
 |   ~   X   /   |   /   /   /   |   X   /   ~   |
 |   *   *   .   |   .   .   .   |   *   .   *   |
 |---------------+---------------+---------------|
 |   *   *   .   |   .   .   .   |   *   .   *   |
 |   *   *   .   |   .   .   .   |   *   .   *   |
 |   *   *   .   |   .   .   .   |   *   .   *   |
 +-----------------------------------------------+

Code: Select all
 finned Jellyfish r1245/c1279 and "~" cells empty in candidate grid
 -- potential Broken Wing pattern
 -- eliminations can not all be false
 -- at least one fin cell must be true   (valid assumption ???)
 +-----------------------------------------------+
 |   ~   X   /   |   /   /   /   |   ~   /   X   |
 |   X   ~   /   |   /   #   /   |   X   /   ~   |
 |   *   *   .   |   .   .   .   |   *   .   *   |
 |---------------+---------------+---------------|
 |   X   ~   /   |   #   /   /   |   ~   /   X   |
 |   ~   X   /   |   /   /   #   |   X   /   ~   |
 |   *   *   .   |   .   .   .   |   *   .   *   |
 |---------------+---------------+---------------|
 |   *   *   .   |   .   .   .   |   *   .   *   |
 |   *   *   .   |   .   .   .   |   *   .   *   |
 |   *   *   .   |   .   .   .   |   *   .   *   |
 +-----------------------------------------------+

Now, welcome to ...

Code: Select all
 Obi-Wahn NoFish #6:
 +-----------------------------------+
 |  . X5  .  |  .  .  .  |  .  . X5  |
 | X5  .  .  |  . #5  .  | X5  .  .  |
 |  .  5  .  |  .  5  5  |  .  .  5  |
 |-----------+-----------+-----------|
 | X5  .  .  | #5  .  .  |  .  . X5  |
 |  . X5  .  |  .  . #5  | X5  .  .  |
 |  5  .  .  |  . -5  .  |  5  .  .  |
 |-----------+-----------+-----------|
 |  .  .  .  |  .  .  .  |  .  5  .  |
 |  .  .  5  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  5  5  5  |  .  .  .  |
 +-----------------------------------+

What makes this particularly interesting is that the potential Jellyfish never performs -5r6c5. However, since 5r6c5 is a peer of all three fin cells, then its elimination can be justified (I hope).

I now have an example of a potential Kraken Jellyfish that performs a Broken Wing elimination for NoFish6, but I'm not sure what to do with it.

Whew!!!





Now, someone will tell me that this has already been determined ... and I must have forgotten about it.
Last edited by daj95376 on Thu Feb 27, 2014 6:48 am, edited 2 times in total.
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Re: A revival of Broken Wings

Postby ronk » Thu Feb 27, 2014 2:16 am

daj95376 wrote:What makes this particularly interesting is that the Jellyfish never performs -5r6c5. However, since 5r6c5 is a peer of all three fin cells, then its elimination can be justified (I hope).

I now have an example of a Kraken Jellyfish that performs a Broken Wing elimination for NoFish6, but I'm not sure what to do with it.

Where did Mike Barker say an unfinned kraken fish didn't need a cover sector (weak link) that included the elimination candidate? I've forgotten a lot of stuff over the years, but that not being a requirement is news to me today.
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Re: A revival of Broken Wings

Postby daj95376 » Thu Feb 27, 2014 6:41 am

ronk wrote:Where did Mike Barker say an unfinned kraken fish didn't need a cover sector (weak link) that included the elimination candidate? I've forgotten a lot of stuff over the years, but that not being a requirement is news to me today.

I'm having trouble following your wording. However, ...

My elimination does not result from a fish pattern because it does not meet the EE and PE requirements in TUFG. It results from the invalidity of the occupied vertices in the candidate grid for the potential fish pattern; thus forcing at least one fin cell to be true.

I've updated my post above to include "potential".
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Re: A revival of Broken Wings

Postby Sudtyro2 » Thu Feb 27, 2014 11:02 pm

DAJ's finned Jellyfish solution of NoFish#6 is very interesting because it reveals a major flaw in my understanding of the basic Fin/Fish exclusion rules. My thinking originally was that one could always assume a Fish=Fin(s) strong-link rule.

This was based in part on the current UFG head post that states...
"In an NxN finned fish:
If the unfinned fish component is false, then at least one of the fins is true.
If all the fins are false, then the unfinned fish component is true."

I interpreted these statements as a Fish=Fin(s) strong-link rule. However, the second statement does not hold for DAJ's finned Jellyfish, because the unfinned Jellyfish is already false. If the three fin cells are all set false, then the unfinned Jellyfish is still false! We know this because one can quickly run an AIC through the X-cells that immediately leads to a contradiction. This Jellyfish pattern, which may be a Broken Wing of sorts, therefore does not have a valid solution. Note, however, that all three fin cells are peers of the exclusion cell.

I think JC Van Hay summed it up nicely when he wrote (via PM):
“Just a warning: you cannot write Fish=Fin(s)!
All you can say about a Finned Fish in a valid puzzle: Either the Fish has at least one solution or it has no solution.
In the first case, a candidate "seeing" [both] the Fish and the Fin(s) is excluded. While in the second case, a candidate "seeing" the Fin(s) is excluded.
So, you can only write Fish=Fin(s) in the first case (Fish false => Fin(s) true and Fin(s) false => Fish true, depending on the solution of the base)!”

JC illustrated this argument based on one of his interpretations of the exclusion in DAJ's 7s grid. JC had developed an Xsudo-like SLG and then further analyzed the SLG, in UFG-style, as a finned Starfish. The Starfish had no solution, but the fins were all peers of the EE cell. His full UFG treatment is shown in the hidden text below. RE-EDIT to clarify which interpretation JC used for his analysis.

Perhaps JC's Starfish is also a Broken Wing of sorts.

Hidden Text: Show
Code: Select all
+-------------------+----------------------+-----------------------+
| 6     8(7)  2     | 3     48(7)   9      | 1       5       48(7) |
| 1(7)  3     18    | 2     4578    58(7)  | 89(7)   489     6     |
| 9     5     4     | 78    1       6      | 28(7)   3       278   |
+-------------------+----------------------+-----------------------+
| 2     6     789   | 5     789     4      | 3       789     1     |
| 4     1     789   | 6789  2       3      | 5       6789    789   |
| 5     789   3     | 1     6789    8(7)   | 289(7)  246789  24789 |
+-------------------+----------------------+-----------------------+
| 3     9(7)  69(7) | 4     6789    2      | 89(7)   1       5     |
| 8     4     15    | 79    3       15     | 6       279     279   |
| 1(7)  2     1569  | 6789  5689-7  158(7) | 4       789     3     |
+-------------------+----------------------+-----------------------+

5 Truths = {7R1 7C167 7B7}
7 Links = {7r2679 7c5 7b13}
1 Elimination --> r9c5<>7

Logical interpretation of the elimination :

1. The 5 base sets has at least 1 solution. For example : 7r9c1 on 7C1 and 7B7, 7r7c7 on 7C7, 7r6c6 on 7C6, 7r1c9 on 7R1

2. UFG style:
1. Remove the 2 cover sets 7r9 and 7c5 to decompose the base sets as
Starfish[7r1c29, 7r2c1, 7r26c6, 7r2367c7, 7r7c23]+Fins[7r1c5, 7r9c1, 7r9c6]
2. The Starfish has no solution : r2c1=7->r1c9=7 AND r6c6=7; these 2 placements imply r7c7=7 and a 7 cannot be placed in r7c23!
The Starfish cannot eliminate a candidate as it is false.
Note : there is NO need for a PE for it!
3. As the base has at least one solution and the Starfish is false, there is at least one fin true in each solution of the base.
4. Conclusion : any peer candidate of the fins can be eliminated.
Last edited by Sudtyro2 on Fri Feb 28, 2014 5:53 pm, edited 2 times in total.
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Re: A revival of Broken Wings

Postby eleven » Fri Feb 28, 2014 9:20 am

Sudtyro2 wrote:Perhaps JC's Starfish is also a Broken Wing of sorts.

I am not familiar with your concepts, but
there is a broken wing (r1c25,r2c1,r9c15), where 7 of the 8 guardians see r9c5 directly.
If 7r1c9, a jellyfish in c1267 (r2679) is left, which would eliminate it.
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Re: A revival of Broken Wings

Postby daj95376 » Fri Feb 28, 2014 6:40 pm

Sudtyro2 wrote:This was based in part on the current UFG head post that states...
"In an NxN finned fish:
If the unfinned fish component is false, then at least one of the fins is true.
If all the fins are false, then the unfinned fish component is true."

There has been tons of rhetoric on defining fish patterns and deriving properties associated with them. I'm not going to tackle all of them.

In the case of your quote, I ask: How often have you seen someone present a finned fish pattern and categorically state that the unfinned fish component is true/false when applied to a candidate grid? Your quote is a derived property that's seldom seen the light in practical applications.

In almost all cases for NxN Fish-based solutions, the logic boils down to:

If a fish pattern is unfinned in the candidate grid, then all of the PE cells for the fish become EE cells in the candidate grid. Otherwise, the EE cells are derived from those PE cells that are seen, either directly or indirectly, by all fin cells.

If you further check TUFG's head post, you'll see that all PE (and thus EE) cells are in the cover set. That's because no one ever expected anyone to state anything categorically about the unfinned fish component!

In my example above, my EE cell is not a PE cell in the cover set for the unfinned fish component. That's because I was able to show that the fish pattern, when applied to the candidate grid, could not be true outside the fin cells.


eleven, nice find! Now, can you reduce it to an invalid unfinned fish component where the fin cells see the elimination cell?
Last edited by daj95376 on Mon Mar 03, 2014 6:54 am, edited 1 time in total.
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Re: A revival of Broken Wings

Postby eleven » Fri Feb 28, 2014 7:12 pm

daj95376 wrote:eleven, nice find! Now, can you reduce it to an invalid unfinned fish component where the fin cells see the elimination cell?

Thanks. Sorry, as i said, i did not read already,what that is.
My elimination in fact is an almost kite combined with an almost jellyfish, but this a broken wing thread :)
Kite(7r1c25,r29c1)=7r1c9-7(r1c2,r3c7)=Jellyfish(7c1267r2679) => r9c5<>7
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Re: A revival of Broken Wings

Postby Sudtyro2 » Fri Feb 28, 2014 9:47 pm

DAJ,
As always, thx for the comments! I fully agree with what you are saying, but I couldn't help but notice that you have qualified your responses with terms like "potential," "seldom seen," "almost all cases," "how often," and "no one ever expected." :)

I find it curious that the UFG apparently makes no mention of the possibility of a false (invalid) unfinned Fish. And, outside of your finned-Jellyfish solution of NoFish#6, I had only been made aware of this possibility through JC Van Hay's UFG-style analysis of his SLG solution of your 7s grid. Maybe seldom seen, but impressive to this tyro, nevertheless. :!:
Edit to qualify the term "false."
Last edited by Sudtyro2 on Mon Mar 03, 2014 9:19 pm, edited 1 time in total.
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Re: A revival of Broken Wings

Postby David P Bird » Sat Mar 01, 2014 12:26 am

Sudtyro2, please think about this:

A simple N-fish with no fins must provide truths in a set of N lines (say rows) which can only occupy cells in N cross-lines (say columns).

If that fish can only hold N-1 truths without producing a contradiction, then one row must be left without the fish digit which would make the puzzle invalid.

For the puzzle to be valid, to be able to satisfy that final row there must be an instance of the digit in a non-fish column - ie there must be a fin somewhere.

There is therefore a strong link between the fish cells holding N truths and the fin cells holding at least one truth.

From that start point the argument can be extended to base and cover sets to make this a general theorem.

DPB
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