Pandiagonal #1

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Re: Pandiagonal #1

Postby Mathimagics » Mon Jun 07, 2021 7:42 am

.
Just wanted to mention that I have corrected a blunder in the post above where I confirmed that creint's 13-clue puzzle was minimal, but then wandered off the reservation and somehow decided that it wasn't!! Go figure ... :?
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Re: Pandiagonal #1

Postby denis_berthier » Mon Jun 07, 2021 11:37 am

.
I've tried to delete candidates from the original puzzle (solvable in Z3):
Code: Select all
.....9...CD.....2.........A.8..5...9..........2......A......1.............3......4........1..........CD.3...9..........D...........6.............A.6..............B..57..



I've found several variants solvable in W3 (I've given one already). But my goal was to find one requiring longer whips.
And I've finally found a puzzle in W4:
Code: Select all
. . . . . . . . . . D . .
. . . 2 . . . . . . . . .
A . 8 . . 5 . . . . . . .
. . . . . . . 2 . . . . .
. A . . . . . . 1 . . . .
. . . . . . . . . 3 . . .
. . . 4 . . . . . . . . 1
. . . . . . . . . . C D .
. . . . 9 . . . . . . . .
. . D . . . . . . . . . .
. 6 . . . . . . . . . . .
. . A . 6 . . . . . . . .
. . . . . . B . . . . . .

..........D.....2.........A.8..5..............2......A......1.............3......4........1..........CD.....9..........D...........6.............A.6..............B......


As you can see, 6 givens have been deleted.

Solution:
(solve "..........D.....2.........A.8..5..............2......A......1.............3......4........1..........CD.....9..........D...........6.............A.6..............B......")

whip[1]: r3n13{c8 .} ==> r6c5 ≠ 13, r13c5 ≠ 13
Code: Select all
Resolution state after Singles and whips[1]:
12345679BC  1245789BC   134579BC    136789AB    457B        2346789C    2345789AC   1346789AC   23456789ABC 125678ABC   D           12345789BC  2345678ABC
1456789BCD  134579BCD   1345679BC   2           3478        4789BC      1346789ACD  345789ABC   356789ACD   1456789ABC  134578AB    35678BC     3456789BCD
A           123479BCD   8           3679C       1347BCD     5           479C        13679BCD    3479BC      12479C      23467B      123467BC    2679BC
1356789BC   134579BD    345679C     135679ABCD  13478ABCD   1346789ABCD 136789AD    2           345789ABC   4578ABC     13456789    1456789ABC  34578BCD
34567BD     A           2345679BC   36789BCD    23457BCD    236789BCD   3456789C    34789B      1           2456789BCD  245789B     2345789C    23456789BCD
2456789C    124578BCD   12679BC     156789BCD   12578ABC    14679ABC    1245789AC   45678ABCD   246789BD    3           1245789B    245789ABC   45679AD
2356789CD   23789BCD    23567BC     4           3578BC      23789ABC    23567ACD    356789BCD   56789ABCD   2789BD      5789B       35679AB     1
234789B     12345789    1235679B    135678AB    123578B     234678B     123456789   145679AB    2345789B    1456789AB   C           D           23456789AB
12345678BCD 23578BC     134567C     13578ABC    9           123678BC    1245678CD   134578BCD   234567ABCD  14567ABD    345678      1234678AB   478BC
5789BC      1345789BC   D           35678AC     1234578BC   124678ABC   1235789C    13456789BC  345679AB    245679C     123456789AB 1346789ABC  2346789AB
134789B     6           23457BC     35789BC     124578ACD   1234789BCD  1234578ACD  13579B      2345789C    1245789ABCD 123479AB    12345789ABC 35789ABCD
1345789BC   23478BD     A           15789BCD    6           1234789CD   134579D     34578C      235789BC    124789BCD   12345789B   123579BC    345789BC
2345678CD   1345789CD   124679      5789C       1234578AC   3479A       B           13456789ACD 234678ACD   1256789C    12356789    13456789AC  234579AC

First steps in W3: Show
z-chain[2]: r3n13{c8 c2} - c6n13{r12 .} ==> r11c13 ≠ 13
z-chain[2]: r8n10{c13 c10} - r9n10{c10 .} ==> r4c4 ≠ 10
t-whip[2]: c13n13{r6 r5} - c6n13{r5 .} ==> r4c2 ≠ 13
t-whip[2]: d13n13{r13c1 r7c7} - a4n13{r7c10 .} ==> r13c2 ≠ 13
whip[2]: c11n10{r11 r10} - r9n10{c10 .} ==> r13c13 ≠ 10
whip[2]: c11n10{r11 r10} - a4n10{r9c12 .} ==> r11c7 ≠ 10
z-chain[3]: r13n13{c8 c9} - d10n13{r2c9 r4c7} - d13n13{r12c2 .} ==> r7c8 ≠ 13
z-chain[2]: d1n13{r5c10 r6c9} - a12n13{r6c4 .} ==> r2c7 ≠ 13
whip[2]: d1n13{r5c10 r6c9} - a10n13{r13c9 .} ==> r5c13 ≠ 13
whip[2]: c13n13{r6 r4} - c6n13{r11 .} ==> r2c9 ≠ 13
z-chain[2]: d10n13{r5c6 r3c8} - r13n13{c8 .} ==> r4c5 ≠ 13
whip[1]: a2n13{r13c1 .} ==> r5c1 ≠ 13
z-chain[2]: d5n13{r12c7 r6c13} - d1n13{r6c9 .} ==> r12c10 ≠ 13
z-chain[2]: c10n13{r11 r5} - r2n13{c13 .} ==> r9c8 ≠ 13
whip[1]: c8n13{r13 .} ==> r3c5 ≠ 13
z-chain[2]: a3n13{r6c8 r7c9} - c5n13{r11 .} ==> r6c4 ≠ 13
whip[1]: a12n13{r9c7 .} ==> r2c1 ≠ 13
whip[1]: r2n13{c13 .} ==> r4c13 ≠ 13
whip[1]: c13n13{r6 .} ==> r6c9 ≠ 13
whip[1]: a4n13{r12c2 .} ==> r7c7 ≠ 13
whip[1]: d3n13{r11c6 .} ==> r7c2 ≠ 13
biv-chain[2]: c5n13{r5 r11} - a12n13{r9c7 r2c13} ==> r5c10 ≠ 13, r2c2 ≠ 13
hidden-single-in-a-row ==> r2c13 = 13
whip[1]: r6n13{c8 .} ==> r13c8 ≠ 13, r12c2 ≠ 13
whip[1]: c2n13{r6 .} ==> r11c7 ≠ 13, r11c10 ≠ 13
whip[1]: r11n13{c6 .} ==> r12c6 ≠ 13
whip[1]: a8n13{r11c5 .} ==> r7c9 ≠ 13
whip[3]: c11n10{r11 r2} - d10n10{r2c9 r11c13} - c10n10{r1 .} ==> r4c5 ≠ 10
z-chain[2]: a2n10{r11c12 r6c7} - c11n10{r2 .} ==> r11c10 ≠ 10
whip[3]: r7n10{c12 c7} - a2n10{r6c7 r11c12} - d2n10{r4c12 .} ==> r10c9 ≠ 10
whip[3]: a2n10{r11c12 r6c7} - d5n10{r9c10 r13c6} - r4n10{c6 .} ==> r9c12 ≠ 10
z-chain[2]: r9n10{c10 c9} - c11n10{r11 .} ==> r6c7 ≠ 10
z-chain[2]: a4n10{r10c13 r1c4} - c5n10{r13 .} ==> r11c13 ≠ 10
t-whip[2]: a4n10{r4c7 r10c13} - a2n10{r11c12 .} ==> r1c10 ≠ 10
whip[2]: d10n10{r6c5 r4c7} - d13n10{r7c7 .} ==> r6c13 ≠ 10
z-chain[2]: d5n10{r13c6 r7c12} - c7n10{r2 .} ==> r4c10 ≠ 10
whip[2]: a4n10{r10c13 r1c4} - a7n10{r6c12 .} ==> r4c6 ≠ 10
z-chain[2]: a3n10{r8c10 r10c12} - r11n10{c12 .} ==> r8c8 ≠ 10
z-chain[2]: a3n10{r10c12 r7c9} - c5n10{r11 .} ==> r6c12 ≠ 10
whip[1]: a7n10{r13c6 .} ==> r13c8 ≠ 10
z-chain[2]: a7n10{r2c8 r13c6} - r9n10{c10 .} ==> r1c9 ≠ 10
z-chain[2]: a9n10{r4c12 r9c4} - d5n10{r9c10 .} ==> r13c12 ≠ 10
z-chain[2]: r13n10{c9 c6} - r9n10{c10 .} ==> r4c9 ≠ 10
z-chain[2]: d12n10{r7c6 r9c4} - d11n10{r2c10 .} ==> r10c6 ≠ 10
z-chain[2]: a10n10{r8c4 r13c9} - r9n10{c9 .} ==> r2c10 ≠ 10
whip[1]: c10n10{r9 .} ==> r9c9 ≠ 10
biv-chain[2]: c10n10{r8 r9} - a9n10{r9c4 r4c12} ==> r10c12 ≠ 10, r7c9 ≠ 10
whip[1]: c9n10{r13 .} ==> r1c8 ≠ 10, r2c7 ≠ 10, r2c11 ≠ 10
whip[1]: c11n10{r11 .} ==> r11c12 ≠ 10
biv-chain[2]: a3n10{r8c10 r6c8} - d9n10{r2c8 r10c13} ==> r8c13 ≠ 10, r1c4 ≠ 10
whip[1]: r1n10{c13 .} ==> r7c7 ≠ 10
whip[1]: r7n10{c12 .} ==> r13c6 ≠ 10
whip[1]: c6n10{r7 .} ==> r6c5 ≠ 10
whip[1]: c13n10{r10 .} ==> r10c4 ≠ 10
biv-chain[3]: r4n10{c7 c12} - r9n10{c4 c10} - d5n13{r9c10 r12c7} ==> r4c7 ≠ 13
19 singles
whip[1]: d5n1{r11c8 .} ==> r10c8 ≠ 1, r4c1 ≠ 1
whip[3]: d5n1{r11c8 r4c2} - r3n1{c2 c12} - d10n1{r12c12 .} ==> r8c5 ≠ 1
z-chain[3]: d5n1{r11c8 r4c2} - c5n1{r4 r10} - r3n1{c12 .} ==> r11c10 ≠ 1
whip[3]: c5n1{r10 r6} - r3n1{c5 c10} - c11n1{r2 .} ==> r10c12 ≠ 1
whip[3]: d5n1{r4c2 r11c8} - d8n1{r6c3 r4c5} - d7n1{r3c5 .} ==> r9c7 ≠ 1
whip[3]: r3n1{c12 c10} - a12n1{r12c10 r6c4} - r1n1{c4 .} ==> r13c2 ≠ 1
whip[3]: d5n1{r4c2 r11c8} - r13n1{c10 c3} - a10n1{r10c6 .} ==> r1c12 ≠ 1
whip[3]: a12n1{r13c11 r4c2} - a6n1{r10c2 r2c7} - a2n1{r6c7 .} ==> r12c11 ≠ 1
whip[3]: d5n1{r11c8 r4c2} - d9n1{r8c2 r11c12} - r10n1{c11 .} ==> r9c6 ≠ 1
whip[3]: a3n1{r12c1 r1c3} - a11n1{r10c7 r11c8} - d4n1{r11c7 .} ==> r3c10 ≠ 1
t-whip[3]: r3n1{c12 c2} - d5n1{r4c2 r11c8} - r8n1{c8 .} ==> r10c5 ≠ 1
z-chain[2]: r10n1{c11 c7} - d5n1{r11c8 .} ==> r1c2 ≠ 1
whip[2]: r3n1{c12 c5} - a2n1{r10c11 .} ==> r11c7 ≠ 1
t-whip[3]: c5n1{r6 r4} - d5n1{r4c2 r11c8} - c7n1{r10 .} ==> r3c2 ≠ 1
whip[1]: r3n1{c12 .} ==> r9c12 ≠ 1
z-chain[2]: d7n1{r10c11 r13c8} - d5n1{r11c8 .} ==> r4c5 ≠ 1
z-chain[2]: c5n1{r6 r3} - r4n1{c4 .} ==> r13c11 ≠ 1
z-chain[3]: r3n1{c5 c12} - c11n1{r2 r6} - c5n1{r6 .} ==> r4c4 ≠ 1
whip[3]: d5n1{r11c8 r4c2} - a8n1{r8c2 r12c6} - c4n1{r1 .} ==> r9c8 ≠ 1
whip[2]: r9n1{c4 c3} - d8n1{r6c3 .} ==> r12c4 ≠ 1
z-chain[2]: r12n1{c10 c12} - r3n1{c12 .} ==> r8c10 ≠ 1
t-whip[2]: r9n1{c4 c3} - d4n1{r12c6 .} ==> r6c4 ≠ 1
z-chain[2]: c4n1{r9 r1} - r13n1{c3 .} ==> r2c10 ≠ 1
whip[2]: d5n1{r4c2 r11c8} - d9n1{r13c10 .} ==> r10c2 ≠ 1
z-chain[2]: a6n1{r6c11 r9c1} - a2n1{r11c12 .} ==> r2c11 ≠ 1
z-chain[2]: c11n1{r10 r4} - d5n1{r4c2 .} ==> r10c7 ≠ 1
biv-chain[2]: r10n1{c11 c6} - r3n1{c12 c5} ==> r13c8 ≠ 1
biv-chain[2]: r3n1{c12 c5} - r10n1{c11 c6} ==> r1c10 ≠ 1
whip[1]: c10n1{r13 .} ==> r6c3 ≠ 1
whip[1]: a11n1{r13c10 .} ==> r11c12 ≠ 1
biv-chain[2]: a10n1{r10c6 r3c12} - c5n1{r3 r6} ==> r2c1 ≠ 1, r6c6 ≠ 1
whip[1]: d11n1{r13c12 .} ==> r13c3 ≠ 1
whip[3]: r7n2{c3 c7} - c1n2{r1 r6} - d4n2{r5c13 .} ==> r8c2 ≠ 2
whip[3]: d6n2{r11c9 r10c10} - a8n2{r3c10 r7c1} - a6n2{r9c1 .} ==> r11c6 ≠ 2
whip[3]: d3n2{r10c7 r5c12} - c5n2{r5 r10} - a1n2{r1c1 .} ==> r6c7 ≠ 2
whip[3]: d6n2{r1c6 r10c10} - d12n2{r13c13 r8c5} - c13n2{r3 .} ==> r1c9 ≠ 2
whip[3]: d12n2{r13c13 r1c12} - d6n2{r11c9 r6c1} - d8n2{r8c1 .} ==> r13c10 ≠ 2
whip[3]: d6n2{r1c6 r11c9} - r13n2{c11 c3} - a10n2{r7c3 .} ==> r1c1 ≠ 2
whip[3]: c1n2{r9 r6} - c9n2{r11 r13} - c3n2{r6 .} ==> r8c13 ≠ 2


This is where it gets harder, with a whip of length 4: Show
whip[4]: c13n2{r5 r13} - c5n2{r5 r10} - a4n2{r6c9 r9c12} - a8n2{r5c12 .} ==> r3c2 ≠ 2
whip[3]: d3n2{r10c7 r5c12} - r3n2{c12 c13} - d12n2{r13c13 .} ==> r10c11 ≠ 2
whip[3]: c5n2{r10 r5} - r10n2{c10 c6} - a2n2{r5c6 .} ==> r8c7 ≠ 2
whip[3]: c7n2{r11 r7} - c2n2{r12 r9} - r13n2{c11 .} ==> r10c6 ≠ 2
whip[3]: c5n2{r10 r5} - r10n2{c10 c7} - c11n2{r6 .} ==> r8c3 ≠ 2
whip[3]: d12n2{r13c13 r1c12} - r13n2{c11 c9} - r8n2{c9 .} ==> r3c13 ≠ 2
z-chain[2]: r3n2{c12 c11} - a13n2{r12c11 .} ==> r1c10 ≠ 2
z-chain[2]: r3n2{c12 c11} - c13n2{r5 .} ==> r1c12 ≠ 2
z-chain[2]: c13n2{r13 r5} - r10n2{c5 .} ==> r7c7 ≠ 2
z-chain[2]: r7n2{c3 c2} - d2n2{r1c2 .} ==> r5c3 ≠ 2
t-whip[2]: a10n2{r11c7 r13c9} - c3n2{r13 .} ==> r11c12 ≠ 2
t-whip[2]: r10n2{c7 c10} - d12n2{r13c13 .} ==> r9c6 ≠ 2
z-chain[3]: a2n2{r8c9 r1c2} - c6n2{r1 r8} - r3n2{c11 .} ==> r5c12 ≠ 2
whip[2]: c12n2{r9 r12} - r13n2{c13 .} ==> r6c9 ≠ 2
z-chain[2]: d1n2{r10c5 r3c12} - d12n2{r3c10 .} ==> r5c5 ≠ 2
z-chain[2]: c5n2{r10 r8} - r10n2{c7 .} ==> r6c1 ≠ 2
z-chain[2]: d6n2{r11c9 r1c6} - a8n2{r12c6 .} ==> r11c10 ≠ 2
z-chain[2]: r11n2{c9 c3} - a4n2{r12c2 .} ==> r9c7 ≠ 2
z-chain[2]: a12n2{r13c11 r8c6} - c3n2{r11 .} ==> r13c9 ≠ 2
z-chain[2]: a10n2{r11c7 r3c12} - a4n2{r9c12 .} ==> r11c3 ≠ 2
z-chain[2]: d1n2{r10c5 r3c12} - r11n2{c7 .} ==> r10c10 ≠ 2
whip[1]: d6n2{r11c9 .} ==> r8c6 ≠ 2
whip[1]: d13n2{r12c2 .} ==> r12c11 ≠ 2
whip[1]: d9n2{r9c1 .} ==> r7c1 ≠ 2
whip[1]: r7n2{c3 .} ==> r6c3 ≠ 2
whip[1]: a11n2{r12c9 .} ==> r8c9 ≠ 2
whip[1]: c9n2{r12 .} ==> r12c10 ≠ 2
whip[1]: c10n2{r5 .} ==> r3c12 ≠ 2
whip[1]: c12n2{r12 .} ==> r9c2 ≠ 2
whip[1]: d1n2{r10c5 .} ==> r5c13 ≠ 2
whip[1]: a2n2{r5c6 .} ==> r1c6 ≠ 2, r5c11 ≠ 2
13 singles
whip[1]: d3n1{r6c11 .} ==> r2c7 ≠ 1
whip[1]: a9n1{r9c4 .} ==> r9c3 ≠ 1
whip[3]: r3n6{c13 c4} - c11n6{r10 r13} - r4n6{c11 .} ==> r9c6 ≠ 6
whip[3]: a10n6{r5c1 r13c9} - c8n6{r1 r10} - d9n6{r6c4 .} ==> r1c1 ≠ 6
whip[4]: d5n6{r7c12 r10c9} - c8n6{r10 r8} - d13n6{r8c6 r2c12} - d1n6{r3c12 .} ==> r7c1 ≠ 6
whip[3]: r7n6{c9 c12} - c6n6{r1 r5} - r3n6{c4 .} ==> r8c8 ≠ 6
whip[3]: c8n6{r13 r1} - c4n6{r10 r6} - c6n6{r8 .} ==> r10c11 ≠ 6
whip[3]: d9n6{r9c1 r13c10} - c11n6{r13 r4} - a10n6{r3c12 .} ==> r6c1 ≠ 6
whip[3]: c11n6{r13 r4} - c1n6{r4 r5} - r7n6{c12 .} ==> r9c7 ≠ 6
z-chain[3]: r9n6{c11 c1} - d7n6{r8c13 r13c8} - c11n6{r13 .} ==> r4c3 ≠ 6
whip[3]: r9n6{c11 c3} - c11n6{r4 r13} - d9n6{r6c4 .} ==> r1c6 ≠ 6
z-chain[2]: c6n6{r8 r6} - d7n6{r4c4 .} ==> r8c3 ≠ 6
t-whip[2]: c11n6{r9 r13} - c6n6{r8 .} ==> r9c3 ≠ 6
whip[2]: r9n6{c1 c11} - c10n6{r8 .} ==> r1c9 ≠ 6
z-chain[2]: a9n6{r13c8 r2c10} - c6n6{r6 .} ==> r5c3 ≠ 6
z-chain[2]: a12n6{r10c8 r13c11} - d6n6{r9c11 .} ==> r10c4 ≠ 6
z-chain[2]: a8n6{r4c11 r6c13} - r3n6{c13 .} ==> r7c8 ≠ 6
z-chain[2]: a2n6{r5c6 r3c4} - d7n6{r4c4 .} ==> r5c13 ≠ 6
whip[1]: a9n6{r13c8 .} ==> r13c10 ≠ 6, r13c12 ≠ 6
z-chain[2]: a9n6{r2c10 r13c8} - c3n6{r13 .} ==> r2c12 ≠ 6
whip[1]: d13n6{r8c6 .} ==> r8c7 ≠ 6
z-chain[2]: a11n6{r6c3 r4c1} - a13n6{r2c1 .} ==> r6c13 ≠ 6
biv-chain[2]: r9n6{c1 c11} - a8n6{r4c11 r1c8} ==> r2c7 ≠ 6
z-chain[2]: a8n6{r1c8 r4c11} - c9n6{r6 .} ==> r10c12 ≠ 6
whip[1]: c12n6{r7 .} ==> r5c1 ≠ 6
whip[1]: r5n6{c7 .} ==> r4c7 ≠ 6, r6c6 ≠ 6
whip[1]: c6n6{r8 .} ==> r13c11 ≠ 6
whip[1]: d11n6{r5c7 .} ==> r8c10 ≠ 6
whip[1]: r8n6{c13 .} ==> r1c13 ≠ 6
whip[1]: a13n6{r10c9 .} ==> r7c9 ≠ 6
biv-chain[2]: c12n6{r7 r3} - c11n6{r4 r9} ==> r9c1 ≠ 6
14 singles


After all these Singles, you thought it was over? You couldn't be more wrong. Here is the hardest part: Show
whip[3]: a11n3{r9c6 r12c9} - r13n3{c9 c2} - r10n3{c2 .} ==> r8c6 ≠ 3
whip[3]: r3n3{c9 c4} - d8n3{r4c5 r13c9} - d5n3{r5c1 .} ==> r10c2 ≠ 3
whip[3]: r3n11{c13 c9} - a4n11{r6c9 r5c8} - a10n11{r2c11 .} ==> r1c13 ≠ 11
whip[4]: d2n4{r9c7 r5c11} - d7n4{r10c11 r2c6} - r3n4{c7 c10} - r8n4{c10 .} ==> r9c8 ≠ 4
whip[4]: r3n11{c13 c2} - c8n11{r9 r7} - d5n11{r7c12 r1c5} - c10n11{r1 .} ==> r5c11 ≠ 11
whip[4]: r3n11{c13 c2} - d2n11{r2c1 r8c8} - r6n11{c6 c11} - r2n11{c11 .} ==> r12c9 ≠ 11
whip[4]: r3n11{c13 c9} - a4n11{r6c9 r12c2} - a12n11{r4c2 r1c12} - d5n11{r7c12 .} ==> r5c13 ≠ 11
whip[4]: r3n4{c10 c9} - r13n4{c9 c8} - c10n4{r11 r10} - d1n4{r1c1 .} ==> r8c2 ≠ 4
whip[4]: r3n3{c9 c2} - c13n3{r1 r11} - r12n3{c13 c8} - a4n3{r5c8 .} ==> r8c9 ≠ 3
whip[3]: r8n3{c7 c2} - r7n3{c2 c12} - c6n3{r1 .} ==> r10c5 ≠ 3
whip[4]: c6n3{r13 r1} - r3n3{c4 c2} - d5n3{r4c2 r5c1} - d3n3{r5c12 .} ==> r11c4 ≠ 3
whip[4]: d5n9{r13c6 r4c2} - d8n9{r7c2 r2c7} - c6n9{r1 r11} - c3n9{r1 .} ==> r6c12 ≠ 9
whip[4]: r3n3{c9 c4} - c6n3{r1 r11} - a4n3{r11c1 r5c8} - d4n3{r10c8 .} ==> r9c2 ≠ 3
whip[3]: a7n3{r13c6 r3c9} - r7n3{c5 c12} - a12n3{r1c12 .} ==> r13c8 ≠ 3
whip[3]: r13n3{c11 c9} - r3n3{c9 c4} - r10n3{c4 .} ==> r4c2 ≠ 3
whip[4]: d5n3{r7c12 r13c6} - d1n3{r9c6 r8c7} - a11n3{r8c5 r2c12} - c2n3{r12 .} ==> r7c1 ≠ 3
whip[4]: r7n3{c8 c12} - d6n3{r1c6 r12c8} - a11n3{r12c9 r9c6} - d12n3{r8c5 .} ==> r4c5 ≠ 3
whip[3]: d8n3{r13c9 r2c7} - a7n3{r2c8 r3c9} - r7n3{c5 .} ==> r13c2 ≠ 3
t-whip[3]: r3n3{c4 c9} - r13n3{c9 c11} - d7n3{r10c11 .} ==> r4c3 ≠ 3, r1c4 ≠ 3
whip[4]: d8n3{r10c12 r13c9} - a7n3{r3c9 r2c8} - d6n3{r12c8 r3c4} - r10n3{c4 .} ==> r7c12 ≠ 3
whip[1]: d5n3{r13c6 .} ==> r13c9 ≠ 3
z-chain[2]: r7n3{c8 c2} - r3n3{c2 .} ==> r12c13 ≠ 3
whip[3]: c4n3{r10 r9} - d8n3{r7c2 r2c7} - a11n3{r2c12 .} ==> r10c11 ≠ 3
whip[2]: d7n3{r12c9 r5c3} - a3n3{r1c3 .} ==> r12c12 ≠ 3
z-chain[3]: d5n3{r13c6 r5c1} - a1n3{r1c1 r4c4} - a2n3{r3c4 .} ==> r2c8 ≠ 3
z-chain[3]: a7n3{r13c6 r3c9} - r9n3{c3 c1} - d5n3{r5c1 .} ==> r11c6 ≠ 3
z-chain[3]: d8n3{r10c12 r7c2} - d10n3{r8c3 r13c11} - a7n3{r13c6 .} ==> r5c7 ≠ 3
whip[3]: c13n3{r11 r5} - r10n3{c8 c4} - a1n3{r4c4 .} ==> r1c3 ≠ 3
t-whip[3]: a3n3{r11c13 r12c1} - d5n3{r5c1 r13c6} - a11n3{r9c6 .} ==> r11c12 ≠ 3
z-chain[3]: a2n3{r7c8 r2c3} - r3n3{c2 c9} - d5n3{r13c6 .} ==> r12c8 ≠ 3
z-chain[3]: d5n3{r13c6 r5c1} - c8n3{r5 r10} - r13n3{c11 .} ==> r9c6 ≠ 3
z-chain[3]: c6n3{r13 r1} - r11n3{c3 c13} - r13n3{c11 .} ==> r5c1 ≠ 3


Finally, a quieter end: Show
hidden-single-in-a-diagonal ==> r13c6 = 3
whip[1]: d6n3{r3c4 .} ==> r2c3 ≠ 3
z-chain[2]: d5n9{r7c12 r6c13} - d8n9{r6c3 .} ==> r10c2 ≠ 9
t-whip[2]: a3n3{r12c1 r11c13} - a10n3{r11c7 .} ==> r1c12 ≠ 3
whip[1]: c12n3{r10 .} ==> r10c4 ≠ 3
z-chain[2]: c12n3{r10 r5} - a10n3{r4c13 .} ==> r2c7 ≠ 3
z-chain[2]: a6n3{r9c1 r11c3} - a11n3{r2c12 .} ==> r12c1 ≠ 3
z-chain[2]: c1n3{r9 r11} - r12n3{c2 .} ==> r1c9 ≠ 3
whip[1]: r1n3{c13 .} ==> r8c7 ≠ 3
whip[1]: c7n3{r11 .} ==> r4c13 ≠ 3, r11c1 ≠ 3, r11c13 ≠ 3
hidden-single-in-an-anti-diagonal ==> r10c12 = 3
whip[1]: a11n3{r12c9 .} ==> r4c9 ≠ 3
hidden-single-in-a-column ==> r12c9 = 3
hidden-single-in-an-anti-diagonal ==> r7c5 = 3
hidden-single-in-a-diagonal ==> r3c4 = 3
hidden-pairs-in-a-column: c2{n1 n3}{r2 r8} ==> r8c2 ≠ 9, r8c2 ≠ 8, r8c2 ≠ 7, r8c2 ≠ 5, r2c2 ≠ 12, r2c2 ≠ 11, r2c2 ≠ 9, r2c2 ≠ 7, r2c2 ≠ 5, r2c2 ≠ 4
hidden-pairs-in-a-row: r4{n1 n3}{c7 c11} ==> r4c11 ≠ 9, r4c11 ≠ 8, r4c11 ≠ 7, r4c11 ≠ 5, r4c11 ≠ 4, r4c7 ≠ 9, r4c7 ≠ 8, r4c7 ≠ 7
hidden-pairs-in-a-row: r8{n1 n3}{c2 c3} ==> r8c3 ≠ 11, r8c3 ≠ 9, r8c3 ≠ 7, r8c3 ≠ 5
hidden-pairs-in-a-column: c1{n1 n3}{r1 r9} ==> r9c1 ≠ 12, r9c1 ≠ 11, r9c1 ≠ 8, r9c1 ≠ 7, r9c1 ≠ 5, r9c1 ≠ 4, r1c1 ≠ 12, r1c1 ≠ 11, r1c1 ≠ 9, r1c1 ≠ 7, r1c1 ≠ 5, r1c1 ≠ 4
z-chain[2]: d8n9{r6c3 r7c2} - d5n9{r4c2 .} ==> r6c11 ≠ 9
z-chain[2]: d8n9{r7c2 r2c7} - c6n9{r2 .} ==> r6c1 ≠ 9
t-whip[2]: d8n9{r6c3 r7c2} - d5n9{r7c12 .} ==> r6c7 ≠ 9
whip[2]: r9n4{c7 c13} - d5n4{r6c13 .} ==> r5c3 ≠ 4
z-chain[3]: d8n9{r7c2 r6c3} - d6n9{r4c3 r10c10} - a8n9{r3c10 .} ==> r7c12 ≠ 9
z-chain[2]: d5n9{r6c13 r4c2} - d6n9{r4c3 .} ==> r6c6 ≠ 9
t-whip[2]: d5n9{r4c2 r6c13} - a11n9{r6c3 .} ==> r13c11 ≠ 9, r13c2 ≠ 9
whip[1]: d10n9{r12c12 .} ==> r12c1 ≠ 9
z-chain[2]: r13n9{c10 c4} - c6n9{r2 .} ==> r1c9 ≠ 9
z-chain[2]: r13n9{c10 c4} - c1n9{r10 .} ==> r11c10 ≠ 9
z-chain[2]: d12n9{r5c8 r4c9} - d5n9{r4c2 .} ==> r5c12 ≠ 9
z-chain[2]: c12n9{r12 r1} - d5n9{r4c2 .} ==> r12c13 ≠ 9
z-chain[2]: d11n9{r11c1 r5c7} - a4n9{r5c8 .} ==> r11c4 ≠ 9
whip[1]: d1n9{r8c7 .} ==> r8c9 ≠ 9
z-chain[2]: a7n9{r5c11 r2c8} - r8n9{c8 .} ==> r5c7 ≠ 9
whip[1]: d11n9{r11c1 .} ==> r6c9 ≠ 9
whip[1]: r6n9{c13 .} ==> r3c13 ≠ 9
whip[1]: d1n9{r8c7 .} ==> r8c8 ≠ 9
whip[1]: r8n9{c10 .} ==> r3c2 ≠ 9
biv-chain[2]: c2n9{r7 r4} - r6n9{c13 c3} ==> r2c7 ≠ 9
whip[1]: c7n9{r8 .} ==> r12c11 ≠ 9
whip[1]: r12n9{c12 .} ==> r4c4 ≠ 9
whip[1]: a1n9{r12c12 .} ==> r10c1 ≠ 9
whip[1]: d10n9{r12c12 .} ==> r11c12 ≠ 9
whip[1]: a2n9{r10c11 .} ==> r7c11 ≠ 9, r10c8 ≠ 9
whip[1]: c11n9{r10 .} ==> r5c3 ≠ 9
whip[1]: a12n9{r4c2 .} ==> r4c9 ≠ 9
whip[1]: c9n9{r7 .} ==> r5c11 ≠ 9
25 singles
whip[1]: r6n11{c12 .} ==> r3c9 ≠ 11
whip[1]: r3n11{c13 .} ==> r2c1 ≠ 11
whip[1]: r7n12{c8 .} ==> r13c8 ≠ 12
whip[1]: c11n4{r12 .} ==> r2c1 ≠ 4
whip[1]: c1n4{r12 .} ==> r12c8 ≠ 4
whip[1]: d7n4{r13c8 .} ==> r11c6 ≠ 4
z-chain[2]: d7n8{r11c10 r13c8} - d6n8{r12c8 .} ==> r2c1 ≠ 8
z-chain[2]: a13n8{r11c10 r12c11} - r7n8{c11 .} ==> r13c8 ≠ 8
z-chain[2]: d1n4{r10c5 r13c2} - a4n4{r12c2 .} ==> r6c1 ≠ 4
whip[1]: c1n4{r12 .} ==> r2c11 ≠ 4, r5c7 ≠ 4
whip[1]: c11n4{r12 .} ==> r5c5 ≠ 4
x-wing-in-columns: n4{c1 c11}{r5 r12} ==> r12c13 ≠ 4, r12c2 ≠ 4, r5c12 ≠ 4
w1-tte


I think it's worth thinking about this resolution path, as it will be typical of solutions in W4. Some simplifications can probably be made, as some steps may be unnecessary, but that will not change the general look of the path.
The sheer number of candidates at the start and the corresponding required number of eliminations implies very long resolution paths. When the puzzle requires whips of length ≥ 3 or 4, it makes a solution extremely boring, exactly as in the case of Sudoku[16].
Whereas finding whips[4] in Sudoku[9] is relatively easy, it seems to me unrealistic to expect manual solvers to find enough of them to obtain a solution.
Pandiagonal Latin Squares seem to be condemned to easy and boring cases.

But the game might become to create puzzles solvable with only whips[1 or 2] and Subsets.
Last edited by denis_berthier on Thu Jun 10, 2021 7:18 am, edited 2 times in total.
denis_berthier
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Re: Pandiagonal #1

Postby creint » Mon Jun 07, 2021 6:36 pm

After
Code: Select all
x-wing-in-columns: n4{c1 c11}{r5 r12} ==> r12c13 ≠ 4, r12c2 ≠ 4, r5c12 ≠ 4
stte

There are still some locked singles so stte is not enough.
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Re: Pandiagonal #1

Postby denis_berthier » Tue Jun 08, 2021 2:16 am

creint wrote:After
Code: Select all
x-wing-in-columns: n4{c1 c11}{r5 r12} ==> r12c13 ≠ 4, r12c2 ≠ 4, r5c12 ≠ 4
stte

There are still some locked singles so stte is not enough.

Right. I meant w1-tte.
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