The New Sudoku Players' Forum

by **Steve R** » Mon Jun 12, 2006 2:22 pm

You are quite right, Havard. I mixed up your whale with another fish when writing early this morning and apologise for it.

I think the squirmbag you found to make the same elimination is the one I set out in my May 28 post. The dual on rows 1, 2, 3, 6 and 7 is also given there. The theory preceding the examples covers the squirmbag eliminations but not that of the whale.

As I now look at it it, we are using the same approach except that you permit cannibalism and I do not. Since I cannot see how to start on a general approach to the cannibalistic eliminations which may arise I am happy to pass on the baton.

Regards

Steve

by **Mike Barker** » Thu Aug 03, 2006 2:52 am

I know I'm 0 for 3 in proposed squirm bags, but here's another set. They came as somewhat of a surprise when I implemented a fishy form of almost constraint subsets (set A is n rows or columns and set B is a combination of n boxes and columns or rows). The result are super Franken fish which, according to Havard, include 2 boxes in the "B" set instead of the usual one which is why I haven't seen them before. So what do you fishermen think?

Code: Select all: #1 Constraint Squirmbag: Base={r34789}, Cover={c478,b78}, fin=r4c9 r3c478|r4c479|r7c24678|r8c37|r9c24567 => r56c8<>5,r6c7<>5 .3.4..9..5......8..74.81....2..37.4....9..2..7..2....9..3.6...8.8.723..1.......6. +------------------+-------------------+------------------+ | 168 3 128 | 4 57 256 | 9 17 567 | | 5 16 12 | 36 79 269 | 1467 8 34 | | 9 7 4 | *356 8 1 | *356 *235 23 | +------------------+-------------------+------------------+ | 168 2 9 | *1568 3 7 | *1568 4 *56 | | 3 1456 1568 | 9 145 4568 | 2 -157 567 | | 7 1456 1568 | 2 145 4568 | -13568 -135 9 | +------------------+-------------------+------------------+ | 124 *159 3 | *15 6 *459 | *457 *257 8 | | 46 8 *56 | 7 2 3 | *45 9 1 | | 124 *159 7 | *158 *1459 *4589 | *345 6 234 | +------------------+-------------------+------------------+ #2 Constraint Squirmbag: r1c345|r5c346|r7c28|r8c57|r9c145 => r4c4<>7 Base={r15789}, Cover={c345,b79}, fin=r5c6 5....2...........493..4.6.7....9....2.....5.3..9..14.....2.8..6.5.4......98..6... +----------------+-----------------+--------------+ | 5 468 *467 | *137 *167 2 | 138 138 9 | | 78 2 67 | 9 1367 37 | 138 5 4 | | 9 3 1 | 8 4 5 | 6 2 7 | +----------------+-----------------+--------------+ | 478 468 5 | -367 9 347 | 17 16 2 | | 2 1 *467 | *67 8 *47 | 5 9 3 | | 3 67 9 | 5 2 1 | 4 67 8 | +----------------+-----------------+--------------+ | 1 *47 3 | 2 5 8 | 9 *47 6 | | 6 5 2 | 4 *37 9 | *378 38 1 | | *47 9 8 | *137 *137 6 | 2 34 5 | +----------------+-----------------+--------------+ #3 Constraint Squirmbag: r1c389|r4c378|r7c1469|r8c12489|r9c249 => r6c8<>1 Base={r14789}, Cover={c389,b78}, fin=r4c7 8....9...2..75..9...4...32..9.47........6..72..7.....5..2....3...5...8......86... +------------------+---------------+------------------+ | 8 7 *136 | 2 34 9 | 5 *146 *146 | | 2 136 136 | 7 5 34 | 146 9 8 | | 9 5 4 | 6 1 8 | 3 2 7 | +------------------+---------------+------------------+ | 5 9 *168 | 4 7 2 | *16 *168 3 | | 134 134 138 | 589 6 135 | 149 7 2 | | 1346 2 7 | 189 39 13 | 1469 -148 5 | +------------------+---------------+------------------+ | *16 8 2 | *159 49 *145 | 7 3 *169 | | *1346 *1346 5 | *139 2 7 | 8 *146 *1469 | | 7 *134 9 | *13 8 6 | 2 5 *14 | +------------------+---------------+------------------+ #4 Constraint Squirmbag: r1c69|r3c5689|r4c478|r7c2389|r8c349 => r6c8<>7, r56c9<>7 Base={r13478}, Cover={c489,b27}, fin=r4c7 9...3..1.7.5.8.......5..6...42..5......8...6.6..9..2..4...2.1...8...439..56....2. +------------------+----------------+---------------------+ | 9 26 48 | 24 3 *67 | 5 1 *278 | | 7 16 5 | 24 8 16 | 49 34 2349 | | 138 123 348 | 5 *179 *179 | 6 *478 *2478 | +------------------+----------------+---------------------+ | 138 4 2 | *137 6 5 | *789 *378 139 | | 5 1379 139 | 8 147 2 | 47 6 -137 | | 6 137 1378 | 9 147 137 | 2 -34578 -134578 | +------------------+----------------+---------------------+ | 4 *379 *379 | 36 2 38 | 1 *578 *567 | | 2 8 *17 | *167 5 4 | 3 9 *67 | | 13 5 6 | 137 179 389 | 478 2 47 | +------------------+----------------+---------------------+ #5 Constraint Squirmbag: r35678c1|r1367c3|r367c5|r1235c6|r57c9 => r7c2<>5 Base={c13569}, Cover={c567,b12}, fin=r8c1 3..8...296...7.....7......8....2...4..9.1..7....7..3.2......1....1.86...8...92.43 +----------------------+-----------------+---------------+ | 3 145 *45 | 8 6 *145 | 7 2 9 | | 6 289 28 | 29 7 *345 | 45 35 1 | | *12459 7 *245 | 29 *345 *1345 | 456 356 8 | +----------------------+-----------------+---------------+ | 7 135 36 | 56 2 8 | 9 156 4 | | *245 24 9 | 346 1 *345 | 8 7 *56 | | *15 4568 *4568 | 7 *45 9 | 3 156 2 | +----------------------+-----------------+---------------+ | *2459 -23569 *23456 | 34 *345 7 | 1 8 *56 | | *45 345 1 | 345 8 6 | 2 9 7 | | 8 56 7 | 1 9 2 | 56 4 3 | +----------------------+-----------------+---------------+ #6 Constraint Squirmbag: r467c3|r12347c4|r1346c5|r234c8|r12378c9 => r7c7<>1 Base={c34589}, Cover={r467,b23}, fin=r8c9 ..6....2...4.3.8....5...3.......3......96..7..3.2...5..4...8...9....726.2.359...4 +--------------------+---------------------+--------------------+ | 3 1789 6 | *1478 *1578 1459 | 14579 2 *1579 | | 17 1279 4 | *167 3 12569 | 8 *19 *15679 | | 178 12789 5 | *14678 *178 1269 | 3 *149 *1679 | +--------------------+---------------------+--------------------+ | 14567 167 *179 | *1478 *1578 3 | 1469 *149 2 | | 1458 158 2 | 9 6 145 | 14 7 3 | | 1467 3 *179 | 2 *17 14 | 469 5 8 | +--------------------+---------------------+--------------------+ | 1567 4 *17 | *16 2 8 | -1579 3 *1579 | | 9 15 8 | 3 4 7 | 2 6 *15 | | 2 167 3 | 5 9 16 | 17 8 4 | +--------------------+---------------------+--------------------+ #7 Constraint Squirmbag: r1c239|r4c358|r5c24|r6c57|r9c129 => r7c3<>3,r8c2<>3 Base={r14569}, Cover={c239,b56}, fin=r9c1 9..1.765..8......7.....3.1.1....89..4.5.9..7....5....2...9.....7...2...6..4.7..9. +------------------+------------------+-----------------+ | 9 *234 *23 | 1 48 7 | 6 5 *348 | | 356 8 1 | 246 45 9 | 234 23 7 | | 56 457 67 | 26 4568 3 | 248 1 9 | +------------------+------------------+-----------------+ | 1 26 *236 | 7 *346 8 | 9 *34 5 | | 4 *36 5 | *36 9 2 | 18 7 18 | | 8 79 79 | 5 *134 14 | *34 6 2 | +------------------+------------------+-----------------+ | 2356 156 -368 | 9 134 1456 | 7 2348 134 | | 7 -1359 89 | 34 2 145 | 145 348 6 | | *2356 *1356 4 | 8 7 156 | 125 9 *13 | +------------------+------------------+-----------------+ #8 Constraint Squirmbag: r1c3489|r2c458|r5c356|r7c57|r8c49 => r4c5<>3 Base={r12578}, Cover={c345,b39}, fin=r5c6 Dual Base={c26,b6}, Dual Cover={r346}, fin=r5c6 .....62....8..4......52.6..5.....9.29......57..1......4.59...7.....6..1.37....... +--------------+----------------+----------------+ | 1 5 *349 | *38 7 6 | 2 *3489 *348 | | 6 2 8 | *13 *139 4 | 7 *39 5 | | 7 34 349 | 5 2 389 | 6 3489 1 | +--------------+----------------+----------------+ | 5 348 7 | 6 -134 13 | 9 348 2 | | 9 6 *34 | 2 *348 *38 | 1 5 7 | | 2 348 1 | 7 59 59 | 34 6 348 | +--------------+----------------+----------------+ | 4 1 5 | 9 *38 2 | *38 7 6 | | 8 9 2 | *34 6 7 | 5 1 *34 | | 3 7 6 | 148 158 158 | 48 2 9 | +--------------+----------------+----------------+

by **Steve R** » Thu Aug 03, 2006 5:30 pm

Well done indeed, Mike.

According to my way of thinking all your fish target three boxes in the sense that there is potential for eliminations in three boxes. It would be helpful to know which columns and boxes you see as targets for elimination in, say, the first example.

Apart from examples 5 and 6, all are based on five rows and target three columns as well as three boxes. Their duals based on five columns. So m + m* (= fish base + dual base) = 5 + 5 = 10, equalling Havard’s record. As to the exceptions:

Example 5

Base columns: 1, 3, 5, 6, and 9
Target rows: 5, 6 and 7
Target boxes: 1, 2 and 7
Dual fish
Base rows: 1, 2, 3, 4, 8, and 9
Target columns: 2, 4, 7 and 8
Target boxes: 1, 2 and 7

Example 6

Base columns: 3, 4, 5, 8 and 9
Target rows: 2, 3 and 9
Target boxes: 4, 6 and 7
Dual fish
Base rows: 1, 2, 3, 5, 8 and 9
Target columns: 1, 2, 6 and 7
Target boxes: 4, 6 and 7

In these two cases m + m* = 5 + 6 = 11. I cannot find a smaller fish within either so to the best of my belief this establishes a new benchmark of the gargantuan on a 9x9 grid. Congratulations!

Steve

by **ronk** » Thu Aug 03, 2006 10:00 pm

Steve R wrote:Well done indeed, Mike.

Absolutely well done.

Steve R wrote:As to the exceptions:

Example 5

Base columns: 1, 3, 5, 6, and 9
Target rows: 5, 6 and 7
Target boxes: 1, 2 and 7
Dual fish
Base rows: 1, 2, 3, 4, 8, and 9
Target columns: 2, 4, 7 and 8
Target boxes: 1, 2 and 7

Example 6

Base columns: 3, 4, 5, 8 and 9
Target rows: 2, 3 and 9
Target boxes: 4, 6 and 7
Dual fish
Base rows: 1, 2, 3, 5, 8 and 9
Target columns: 1, 2, 6 and 7
Target boxes: 4, 6 and 7

In these two cases m + m* = 5 + 6 = 11. I cannot find a smaller fish within either so to the best of my belief this establishes a new benchmark of the gargantuan on a 9x9 grid.

As long we insist on having only rows or only columns in the base, we won't get to the true dual count M = 9 - P - N ... where P is the number of placements. I see these two puzzles as:

Example 5

Base: columns 1, 3, 5, 6, and 9
Target: rows 5, 6 and 7 AND boxes 1 and 2
Fin: r8c1
Dual fish
Base: rows 4, 8, and 9 AND box 3
Target: columns 2, 4, 7 and 8
Fin: r8c1

Example 6

Base: columns 3, 4, 5, 8 and 9
Target: rows 4, 6 and 7 AND boxes 2 and 3
Fin: r8c9
Dual fish
Base: rows 5, 8 and 9 AND box 1
Target: columns 1, 2, 6 and 7
Fin: r8c9

There are no placements in either puzzle ... and M + N = 9.

by **Havard** » Thu Aug 03, 2006 10:38 pm

ronk wrote:
Example 5
Base: columns 1, 3, 5, 6, and 9
Target: rows 5, 6 and 7 AND boxes 1 and 2
Fin: r8c1

Example 6
Base: columns 3, 4, 5, 8 and 9
Target: rows 4, 6 and 7 AND boxes 2 and 3
Fin: r8c9

This is the same way as I see it.

All the squirmbags Mike posted has this "three lines, two boxes, one fin" - structure.

Havard

by **ronk** » Fri Aug 04, 2006 5:24 pm

Mike Barker, when you're bored to tears with nothing to do

would you consider editing your "almost squirmbag" post to number the puzzles?

And thanks for posting them, Ron

by **ronk** » Fri Oct 06, 2006 4:47 pm

Mike Barker wrote:Here ... if a fish with a big fin appears to be missing a row (column), a so called skinny fish, other reductions are possible. The dashes indicate cells without the candidate (in this case because of Box/Box eliminations):

Code: Select all: . . . | * X * | X X - . . . | * X X | X X * . . . | . . . | X X * . . . | * X * | X X - . . . | * X X | X X * * X * | * X * | * * * . . . | * X * | X X - . . . | * X X | X X * . | . | . | . | X X * -------+---|---+-|-|--- -------+---|-|-+-|-|--- ---|---+---|---+-|-|--- . . . | . | . | | | - . . . | . | | | | | . . | . | . | . | | | . * * * | * * * | X X - * * * | * X X | X X * * X * | * X * | X X * . . . | . | . | | | - . . . | . | | | | | . . | . | . | . | | | . -------+---|---+-|-|--- -------+---|-|-+-|-|--- ---|---+---|---+-|-|--- . . . | . | . | | | . . . . | . | | | | | . . | . | . | . | | | . . . . | . | . | | | . . . . | . | | | | | . . | . | . | . | | | . . . . | . | . | | | . * * * | * X X | X X * * X * | * X * | X X *

Illustrating degenerate cases always seems to be problematic. To be consistent with the other two diagrams, however, I recommend replacing the first with ...

Code: Select all: . . . | * X * | X X * . . . | * X * | X X * . . . | * X * | X X * -------+---|---+-|-|--- . . . | . | . | | | . * * * | * X * | X X * . . . | . | . | | | . -------+---|---+-|-|--- . . . | . | . | | | . . . . | . | . | | | . . . . | . | . | | | .

... along with the caveat, since the pattern is degenerate, those same exclusions (and a couple more) may be made with box/box exclusions in stack 3, followed by locked candidate exclusions in box 6 and then box 2.

by **Myth Jellies** » Sun Oct 22, 2006 8:39 am

Even though I posted this elsewhere, I thought it might be worthwhile to add it to this tank...

Michael Mephem's 4th extreme puzzle has an interesting biggish fish...

Code: Select all: *-----------* |..5|3..|6..| |.2.|.7.|.4.| |...|.1.|..8| |---+---+---| |3..|4..|..1| |.6.|251|.8.| |2..|..8|..4| |---+---+---| |4..|.2.|...| |.7.|.4.|.9.| |..1|..3|4..| *-----------*

Basic methods will take you here...

Code: Select all: *-----------------------------------------------------------------------------* | 179 489 5 | 3 89 24 | 6 127 279 | | 1689 2 3 | 5689 7 569 | 159 4 59 | | 679 49 679 | 569 1 24 | 2579 3 8 | |-------------------------+-------------------------+-------------------------| | 3 5 8 | 4 69 679 | 279 267 1 | | 79 6 4 | 2 5 1 | 379 8 379 | | 2 1 79 | 679 3 8 | 579 567 4 | |-------------------------+-------------------------+-------------------------| | 4 3 69 | 156789 2 5679 | 1578 157 567 | | 568 7 2 | 1568 4 56 | 1358 9 356 | | 569 89 1 | 5679 689 3 | 4 257 2567 | *-----------------------------------------------------------------------------*

Filtering on the sevens we have a swordfish with two distinct fins...

Code: Select all: +-----------+-----------+-----------+ |*7 . . | . . . | . *7 *7 | | . . . | . 7 . | . . . | | 7 . 7 | . . . | 7 . . | +-----------+-----------+-----------+ | . . . | . . A7 | 7 -7 . | |*7 . . | . . . |#7 *. *7 | | . . 7 |a7 . . | 7 7 . | +-----------+-----------+-----------+ | . . . | 7 . a7 | 7 7 7 | | . 7 . | . . . | . . . | |*. . . |#7 . . | . *7 *7 | +-----------+-----------+-----------+

Either the r159c189 swordfish is true, or the fin in r5c7 is true, or the fin in r9c4 is true, which with a little weak then strong link extension would imply A (r4c6) contains a 7. In all three possible cases, seven can be removed from r4c8.

I thought this was an interesting case of an almost finned swordfish.

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