The New Sudoku Players' Forum

[denis_berthier]

.
The first 13x13 Pandiag I posted was based on an acyclic complete grid; the second on a cyclic one.
The 3rd is now based on a semi-cyclic one.
As far as I can see, it doesn't make any difference in terms of generating puzzles or solving them in a pattern-based way.

Code: Select all

1 2 . . 5 6 . 8 . . . C .
. 4 . . . . . . . . . . .
. . . . . . . . . . . . .
. . . . . . . . . . . . .
. . A . . . . . . . . . .
. . . . . . . . . . . . .
. . . . . . . . . . . . .
. . . . . . . . . . . . .
. . . . . . B . D . . . .
. . . . . . D . B . . . .
. . . B D . . . . . . . .
. . . . 9 . . . . . 7 . .
. 9 . . . . . . . C . A .

12..56.8...C..4.......................................A.......................................................B.D..........D.B.......BD............9.....7...9.......C.A.

This puzzle should be easier than my first two.

[Mathimagics]

The 3rd is now based on a semi-cyclic one.

Let's assume I am just a normal P&P puzzler who has solved this puzzle ...

.. and is now wondering: "how on Earth is this solution semicyclic?"

[denis_berthier]

The 3rd is now based on a semi-cyclic one.

Let's assume I am just a normal P&P puzzler who has solved this puzzle ...
.. and is now wondering: "how on Earth is this solution semicyclic?"

The P&P solver doesn't care about cyclicity and doesn't have to know anything about it. Considering the very large number of isomorphisms for 13x13 puzzles, I don't see any way these could be used in practice by a human solver.

I chose 3 different types of initial grids for my examples and I couldn't find any difference in the way I could manually generate "interesting" puzzles or in the way CSP-Rules solved them. [By "interesting", I mean not too obvious and not too hard.]

[m_b_metcalf]

Denis,
Back from a trip, I couldn't resist brushing off and upgrading my old Latin Square solver and trying it out on these 13x13 PDs. I'm happy to say that it solves your three, using mainly contradictions, in 4 to 7 secs. Using a grid from Mathimagics, I've produced a few of my own, and would be grateful if someone could check them as valid. They are at or close to minimality.

Thanks,

Mike

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.........C..3........A......83.....9.........................2.8...9...........7.4.....D.......................B..62..8........9.........1..........2......7...........1.  21
........B.D...3.....9.............C.................7......3...........C............6.9........8...5..D......7...A.......................12..........D....9.......B....1.  21
...84...............................2....................6........D.......3...C.......9...1.........B..6....97.............2............3.............5.1......9.3..85...  21
.....9..B.....3...........A......D.......C..........................6.....3.........6......2......7........1...B....C.....12...............7...4..C.....18..............2  22

[denis_berthier]

Denis,Back from a trip, I couldn't resist brushing off and upgrading my old Latin Square solver and trying it out on these 13x13 PDs. I'm happy to say that it solves your three, using mainly contradictions, in 4 to 7 secs. Using a grid from Mathimagics, I've produced a few of my own, and would be grateful if someone could check them as valid. They are at or close to minimality.
Thanks,
Mike

Code: Select all

.........C..3........A......83.....9.........................2.8...9...........7.4.....D.......................B..62..8........9.........1..........2......7...........1.  21
........B.D...3.....9.............C.................7......3...........C............6.9........8...5..D......7...A.......................12..........D....9.......B....1.  21
...84...............................2....................6........D.......3...C.......9...1.........B..6....97.............2............3.............5.1......9.3..85...  21
.....9..B.....3...........A......D.......C..........................6.....3.........6......2......7........1...B....C.....12...............7...4..C.....18..............2  22

Hi Mike,
These 4 puzzles are valid - and in T&E(1).

The 1st is relatively easy, in W3:

Code: Select all

Resolution state after Singles and whips[1]:
14567ABD    12456ABD    12457A      156789AB    245679ABD   14579ABD    145678ABD   456D        1245689BD   C           25ABD       4567ABD     3           
2456789CD   1234569C    1456BCD     2579BCD     145789BC    1345678BCD  13456BCD    23456789CD  A           3456B       1234578BD   567BCD      14568BCD   
124567AC    456ACD      8           3           1457ABCD    1456ABC     124567ABCD  567D        2456BCD     9           1245ABCD    4567ABD     256ABCD     
35678ABCD   234569ABCD  2457ACD     1567ABCD    124568ABCD  1345789ABCD 1356789B    234569ACD   134567BCD   145678AB    13457BCD    34569ABCD   124569A     
345679ABD   5ABCD       134567ABCD  56ACD       1345679ABCD 156BD       3459ABCD    34567AC     145679BCD   2           13457ABCD   8           14569ABCD   
12458ABCD   13456ABD    9           125678ABCD  25678D      3456ABCD    124568ABCD  24578ACD    1345678BC   1345678AB   13457AC     34567ABCD   456BCD     
1356BC      7           12356AB     4           23569ABC    568AC       12569ABC    568AC       123589BC    D           1358ABC     3569ABC     12589ABC   
1234568ABCD 13456BCD    12356BD     2569ABD     235678ABCD  1456789ABCD 456789ACD   234567ACD   12456C      134578AB    3457ABC     4579ABCD    1456ABCD   
134579ACD   1359D       345CD       158ACD      145789AD    3578ACD     134578ACD   B           134579CD    45A         6           2           1458ACD     
123567BD    8           1234567ABCD 1567BCD     13456ABCD   134567ABD   23567AC     34567ACD    24567CD     1457AB      9           345ABCD     1456ABC     
34569ABC    23456ABCD   4567ABCD    56789ABCD   34567BCD    34569AC     3456789ABD  1           245789BCD   45678A      2345ABCD    456ABCD     2589BD     
13458ABCD   14569ABC    13456ABCD   1569ABCD    134569AC    2           34569ABCD   4589AD      3568BCD     134568AB    458ACD      3569BD      7           
24568ABCD   3459ABCD    34567ABC    25679AC     345679ABCD  345679ABCD  457BCD      34568ACD    234568BD    35678AB     23578BD     1           2456ABCD   

1153 candidates.

The resolution path is similar to the 3 I've posted before: Show

z-chain[2]: r1n8{c9 c7} - a9n8{r13c8 .} ==> r6c4 ≠ 8
z-chain[2]: c4n8{r11 r9} - r1n8{c9 .} ==> r11c7 ≠ 8
z-chain[2]: a13n9{r2c1 r8c7} - c12n9{r8 .} ==> r12c4 ≠ 9
z-chain[2]: c8n9{r12 r2} - a13n9{r2c1 .} ==> r8c4 ≠ 9
z-chain[2]: c4n9{r13 r11} - r13n9{c2 .} ==> r1c5 ≠ 9
z-chain[2]: c8n9{r12 r2} - a13n9{r2c1 .} ==> r8c12 ≠ 9
whip[1]: c12n9{r12 .} ==> r12c7 ≠ 9
whip[1]: r8n9{c7 .} ==> r7c7 ≠ 9
z-chain[2]: a5n9{r5c9 r13c4} - d1n9{r11c4 .} ==> r5c7 ≠ 9
z-chain[2]: r5n9{c13 c1} - d2n9{r2c1 .} ==> r1c9 ≠ 9
whip[1]: a9n9{r11c6 .} ==> r4c13 ≠ 9
whip[1]: r1n9{c6 .} ==> r13c5 ≠ 9, r2c5 ≠ 9
whip[1]: r13n9{c6 .} ==> r2c4 ≠ 9, r11c4 ≠ 9
biv-chain[2]: r8n9{c7 c6} - r1n9{c6 c4} ==> r4c7 ≠ 9, r11c7 ≠ 9
hidden-single-in-a-column ==> r8c7 = 9
whip[1]: r2n9{c8 .} ==> r9c2 ≠ 9, r12c5 ≠ 9, r5c5 ≠ 9
whip[1]: d2n9{r7c9 .} ==> r4c6 ≠ 9, r7c12 ≠ 9
whip[1]: r7n9{c13 .} ==> r11c9 ≠ 9
whip[1]: a12n9{r7c5 .} ==> r4c8 ≠ 9
whip[1]: c8n9{r12 .} ==> r7c13 ≠ 9
whip[1]: c13n9{r11 .} ==> r11c6 ≠ 9
whip[2]: r8n8{c10 c5} - a10n8{r9c5 .} ==> r12c10 ≠ 8
whip[2]: a2n8{r6c7 r4c5} - r8n8{c5 .} ==> r6c8 ≠ 8
z-chain[2]: c8n8{r12 r13} - r11n8{c10 .} ==> r7c13 ≠ 8
whip[2]: c13n8{r9 r11} - a12n8{r2c13 .} ==> r9c6 ≠ 8
z-chain[2]: d1n8{r11c4 r6c9} - r1n8{c4 .} ==> r2c8 ≠ 8
t-whip[2]: a11n8{r13c10 r12c9} - r1n8{c7 .} ==> r8c10 ≠ 8
z-chain[2]: a3n8{r12c1 r11c13} - c11n8{r13 .} ==> r7c6 ≠ 8
whip[2]: a7n8{r11c4 r8c1} - a11n8{r4c1 .} ==> r11c10 ≠ 8
whip[1]: r11n8{c13 .} ==> r2c13 ≠ 8
z-chain[2]: c10n8{r13 r6} - d8n8{r9c13 .} ==> r13c1 ≠ 8
z-chain[2]: a2n8{r6c7 r7c8} - d4n8{r7c11 .} ==> r4c7 ≠ 8
z-chain[2]: a4n8{r6c9 r2c5} - d7n8{r2c6 .} ==> r1c9 ≠ 8
whip[1]: r1n8{c7 .} ==> r11c4 ≠ 8
whip[1]: r11n8{c13 .} ==> r7c9 ≠ 8, r13c11 ≠ 8
whip[1]: r13n8{c10 .} ==> r12c9 ≠ 8
whip[1]: r12n8{c11 .} ==> r2c11 ≠ 8
whip[1]: d1n8{r7c8 .} ==> r6c7 ≠ 8
x-wing-in-columns: n8{c4 c7}{r1 r9} ==> r9c13 ≠ 8, r9c5 ≠ 8
10 Singles
whip[1]: r4n8{c10 .} ==> r8c1 ≠ 8
whip[1]: a10n8{r13c9 .} ==> r13c8 ≠ 8
z-chain[2]: r11n2{c11 c9} - c4n2{r6 .} ==> r2c11 ≠ 2
z-chain[2]: r2n2{c4 c1} - d5n2{r10c9 .} ==> r1c3 ≠ 2
whip[1]: a3n2{r6c8 .} ==> r6c4 ≠ 2
z-chain[2]: a3n2{r6c8 r2c4} - c2n2{r2 .} ==> r6c7 ≠ 2
z-chain[2]: r6n2{c5 c8} - d5n2{r2c4 .} ==> r10c1 ≠ 2
z-chain[2]: r10n2{c7 c9} - c4n2{r2 .} ==> r8c5 ≠ 2
z-chain[2]: r10n2{c9 c3} - a10n2{r7c3 .} ==> r8c9 ≠ 2
z-chain[2]: a2n2{r4c5 r13c1} - a3n2{r6c8 .} ==> r1c5 ≠ 2
whip[1]: d5n2{r10c9 .} ==> r2c1 ≠ 2
z-chain[2]: a5n2{r4c8 r11c2} - r1n2{c2 .} ==> r3c9 ≠ 2
z-chain[2]: a7n2{r8c1 r10c3} - a13n2{r10c9 .} ==> r6c1 ≠ 2
biv-chain[2]: c4n2{r8 r2} - r6n2{c8 c5} ==> r7c5 ≠ 2, r8c3 ≠ 2
whip[1]: c3n2{r10 .} ==> r7c13 ≠ 2
whip[1]: d6n2{r11c9 .} ==> r10c9 ≠ 2
10 Singles
z-chain[2]: r3n1{c7 c1} - a10n1{r4c13 .} ==> r2c6 ≠ 1
whip[3]: a13n7{r11c10 r2c1} - r9n7{c7 c6} - a8n7{r4c11 .} ==> r10c10 ≠ 7
whip[3]: d10n7{r13c11 r4c7} - d6n7{r13c7 r8c12} - r1n7{c12 .} ==> r3c1 ≠ 7
whip[1]: d3n7{r6c11 .} ==> r11c3 ≠ 7, r6c8 ≠ 7
z-chain[3]: r11n7{c10 c5} - c4n7{r10 r6} - d3n7{r6c11 .} ==> r1c7 ≠ 7
z-chain[3]: d3n7{r1c3 r6c11} - d10n7{r3c8 r10c1} - d6n7{r8c12 .} ==> r13c3 ≠ 7
t-whip[3]: d10n7{r13c11 r4c7} - d6n7{r13c7 r8c12} - d13n7{r8c6 .} ==> r10c8 ≠ 7
z-chain[2]: c8n7{r5 r8} - d6n7{r8c12 .} ==> r4c7 ≠ 7
t-whip[2]: d3n7{r1c3 r6c11} - d10n7{r13c11 .} ==> r1c5 ≠ 7, r10c3 ≠ 7, r1c1 ≠ 7
z-chain[3]: d3n7{r6c11 r1c3} - d12n7{r1c12 r4c9} - c8n7{r3 .} ==> r8c11 ≠ 7
whip[1]: d5n7{r13c6 .} ==> r10c6 ≠ 7
whip[1]: r10n7{c9 .} ==> r5c9 ≠ 7
t-whip[2]: d10n7{r13c11 r10c1} - d5n7{r10c9 .} ==> r13c5 ≠ 7
z-chain[3]: c3n7{r5 r4} - a4n7{r2c5 r6c9} - d3n7{r6c11 .} ==> r1c12 ≠ 7
whip[1]: r1n7{c4 .} ==> r8c10 ≠ 7
whip[2]: r1n7{c3 c4} - r11n7{c4 .} ==> r3c5 ≠ 7
whip[1]: a3n7{r4c6 .} ==> r4c3 ≠ 7
z-chain[2]: d6n7{r13c7 r8c12} - c7n7{r3 .} ==> r11c5 ≠ 7
whip[1]: c5n7{r8 .} ==> r5c8 ≠ 7
z-chain[2]: a8n7{r10c4 r13c7} - r11n7{c7 .} ==> r4c10 ≠ 7
z-chain[2]: d13n7{r8c6 r10c4} - d6n7{r13c7 .} ==> r8c5 ≠ 7
whip[1]: d12n7{r4c9 .} ==> r6c11 ≠ 7, r4c11 ≠ 7
hidden-single-in-a-diagonal ==> r1c3 = 7
whip[1]: r4n7{c9 .} ==> r9c9 ≠ 7
biv-chain[2]: d12n7{r4c9 r2c11} - c5n7{r2 r5} ==> r4c4 ≠ 7, r9c1 ≠ 7
whip[1]: r9n7{c7 .} ==> r8c6 ≠ 7
whip[1]: r8n7{c12 .} ==> r6c10 ≠ 7
whip[1]: r6n7{c12 .} ==> r11c4 ≠ 7
whip[1]: d7n7{r11c10 .} ==> r2c1 ≠ 7
whip[1]: a1n7{r8c8 .} ==> r5c11 ≠ 7
biv-chain[2]: d7n7{r11c10 r2c6} - r9n7{c6 c7} ==> r11c7 ≠ 7
hidden-single-in-a-row ==> r11c10 = 7
whip[1]: d4n7{r6c12 .} ==> r2c12 ≠ 7
hidden-single-in-a-diagonal ==> r10c4 = 7
whip[1]: r6n7{c12 .} ==> r3c12 ≠ 7
z-chain[2]: r1n1{c7 c9} - a8n1{r8c2 .} ==> r4c4 ≠ 1
z-chain[2]: a8n1{r8c2 r7c1} - r3n1{c1 .} ==> r4c6 ≠ 1
t-whip[2]: r1n1{c9 c7} - r7n1{c13 .} ==> r9c9 ≠ 1
z-chain[3]: c5n8{r8 r2} - c5n7{r2 r5} - c1n7{r5 .} ==> r4c1 ≠ 8
whip[1]: c1n8{r6 .} ==> r2c5 ≠ 8, r6c10 ≠ 8
biv-chain[3]: r9n8{c7 c4} - r6n8{c1 c9} - d1n7{r6c9 r9c6} ==> r9c7 ≠ 7
8 Singles
whip[1]: c8n3{r13 .} ==> r5c3 ≠ 3
z-chain[2]: a11n3{r13c10 r12c9} - r7n3{c1 .} ==> r13c5 ≠ 3
z-chain[2]: d6n1{r7c13 r10c10} - a3n1{r8c10 .} ==> r7c1 ≠ 1
whip[2]: a8n1{r4c11 r8c2} - c9n1{r1 .} ==> r12c3 ≠ 1
z-chain[3]: r3n1{c6 c5} - r5n1{c5 c11} - a8n1{r4c11 .} ==> r8c6 ≠ 1
t-whip[2]: c6n1{r10 r5} - c3n1{r8 .} ==> r10c13 ≠ 1
whip[2]: r1n1{c9 c7} - d13n1{r7c7 .} ==> r6c9 ≠ 1
t-whip[2]: a8n1{r4c11 r8c2} - c9n1{r8 .} ==> r4c10 ≠ 1, r5c11 ≠ 1, r7c11 ≠ 1
whip[1]: r7n1{c13 .} ==> r1c7 ≠ 1, r10c10 ≠ 1
whip[1]: c11n1{r6 .} ==> r4c13 ≠ 1
z-chain[2]: d13n1{r7c7 r12c2} - r1n1{c4 .} ==> r5c5 ≠ 1
z-chain[2]: a1n1{r2c2 r7c7} - d6n1{r7c13 .} ==> r3c1 ≠ 1
whip[1]: r3n1{c6 .} ==> r4c5 ≠ 1
biv-chain[2]: r4n1{c11 c7} - r3n1{c6 c5} ==> r10c5 ≠ 1
whip[1]: c5n1{r12 .} ==> r12c1 ≠ 1
whip[1]: a3n1{r8c10 .} ==> r8c13 ≠ 1
biv-chain[2]: d6n1{r6c1 r7c13} - c5n1{r12 r3} ==> r6c2 ≠ 1
whip[1]: a10n1{r10c6 .} ==> r10c3 ≠ 1
whip[1]: r10n1{c6 .} ==> r5c6 ≠ 1, r6c10 ≠ 1
biv-chain[2]: a10n1{r10c6 r2c11} - r4n1{c11 c7} ==> r9c7 ≠ 1, r3c6 ≠ 1, r10c1 ≠ 1
6 Singles
hidden-pairs-in-a-column: c4{n1 n8}{r1 r9} ==> r9c4 ≠ 13, r9c4 ≠ 12, r9c4 ≠ 10, r9c4 ≠ 5, r1c4 ≠ 11, r1c4 ≠ 10, r1c4 ≠ 6, r1c4 ≠ 5
whip[2]: a10n3{r13c9 r6c2} - c9n3{r12 .} ==> r11c11 ≠ 3
whip[2]: d8n3{r13c9 r2c7} - a10n3{r11c7 .} ==> r13c2 ≠ 3
whip[2]: d10n3{r10c1 r4c7} - d1n3{r6c9 .} ==> r10c3 ≠ 3
whip[2]: a12n3{r10c8 r9c7} - d10n3{r4c7 .} ==> r10c5 ≠ 3
whip[2]: d1n3{r6c9 r12c3} - d12n3{r11c2 .} ==> r8c11 ≠ 3
t-whip[2]: d5n3{r13c6 r7c12} - d8n3{r10c12 .} ==> r13c8 ≠ 3
z-chain[2]: c8n3{r5 r10} - d8n3{r10c12 .} ==> r2c11 ≠ 3
z-chain[2]: r2n3{c10 c7} - d5n3{r7c12 .} ==> r11c6 ≠ 3
z-chain[2]: d3n3{r6c11 r12c5} - r11n3{c5 .} ==> r6c2 ≠ 3
whip[1]: a10n3{r13c9 .} ==> r9c9 ≠ 3, r2c7 ≠ 3
whip[1]: r2n3{c10 .} ==> r6c6 ≠ 3
whip[1]: a1n3{r5c5 .} ==> r12c5 ≠ 3, r8c2 ≠ 3
hidden-pairs-in-a-diagonal: d3{n1 n3}{a1 a6} ==> d3a6 ≠ 12, d3a6 ≠ 10, d3a6 ≠ 5, d3a6 ≠ 4, d3a1 ≠ 12, d3a1 ≠ 6, d3a1 ≠ 5, d3a1 ≠ 4
biv-chain[2]: a10n3{r13c9 r11c7} - c8n3{r10 r5} ==> r6c9 ≠ 3, r13c3 ≠ 3
whip[1]: a4n3{r5c8 .} ==> r5c7 ≠ 3
whip[1]: r6n3{c11 .} ==> r5c11 ≠ 3, r7c11 ≠ 3
whip[1]: r5n3{c8 .} ==> r8c5 ≠ 3
whip[1]: r8n3{c10 .} ==> r2c10 ≠ 3
whip[1]: d11n3{r9c3 .} ==> r7c1 ≠ 3, r11c5 ≠ 3, r9c7 ≠ 3
whip[1]: a8n3{r9c3 .} ==> r12c3 ≠ 3
26 Singles
whip[1]: d10n11{r10c1 .} ==> r13c1 ≠ 11
whip[1]: r9n10{c13 .} ==> r1c5 ≠ 10, r4c5 ≠ 10
whip[1]: c10n6{r13 .} ==> r1c9 ≠ 6, r2c12 ≠ 6, r13c8 ≠ 6
z-chain[2]: d6n11{r13c7 r8c12} - d4n11{r7c11 .} ==> r13c10 ≠ 11
z-chain[2]: c10n11{r8 r10} - d10n11{r10c1 .} ==> r5c7 ≠ 11
z-chain[2]: a11n6{r13c10 r3c13} - d10n6{r3c8 .} ==> r13c1 ≠ 6
z-chain[2]: r13n6{c10 c5} - a11n6{r4c1 .} ==> r10c13 ≠ 6
z-chain[2]: d10n6{r5c6 r10c1} - c8n6{r10 .} ==> r3c6 ≠ 6
whip[1]: a4n6{r13c3 .} ==> r12c3 ≠ 6
z-chain[2]: a5n6{r11c2 r10c1} - c8n6{r3 .} ==> r1c12 ≠ 6
z-chain[2]: r1n6{c8 c7} - r5n6{c3 .} ==> r4c5 ≠ 6
z-chain[2]: d4n6{r10c8 r13c5} - a11n6{r13c10 .} ==> r3c1 ≠ 6
t-whip[2]: r4n6{c13 c4} - a10n6{r8c4 .} ==> r3c13 ≠ 6
whip[1]: a11n6{r13c10 .} ==> r13c5 ≠ 6
z-chain[2]: d4n6{r4c1 r10c8} - d8n6{r1c8 .} ==> r2c1 ≠ 6
z-chain[2]: c1n6{r7 r10} - r5n6{c6 .} ==> r4c4 ≠ 6
z-chain[2]: r4n6{c13 c1} - c10n6{r13 .} ==> r11c6 ≠ 6
t-whip[2]: r2n6{c13 c7} - c8n6{r3 .} ==> r10c5 ≠ 6
z-chain[2]: a9n6{r12c7 r2c10} - r13n6{c10 .} ==> r12c4 ≠ 6
z-chain[2]: d1n6{r11c4 r2c13} - d3n6{r4c13 .} ==> r3c9 ≠ 6
z-chain[2]: d11n6{r8c4 r2c10} - c13n6{r2 .} ==> r6c2 ≠ 6
t-whip[2]: r3n6{c8 c12} - r4n6{c13 .} ==> r10c8 ≠ 6
whip[1]: c8n6{r3 .} ==> r2c7 ≠ 6
biv-chain[2]: d4n6{r4c1 r3c2} - d8n6{r5c4 r1c8} ==> r7c1 ≠ 6
whip[1]: a8n6{r11c5 .} ==> r1c5 ≠ 6
whip[1]: a5n6{r11c2 .} ==> r10c3 ≠ 6
biv-chain[2]: a5n6{r11c2 r10c1} - d4n6{r4c1 r3c2} ==> r12c2 ≠ 6, r7c6 ≠ 6
w1-tte

What do you mean by "using mainly contradictions"? Do you mean combining them with some form of T&E or DFS?
4 to 7 seconds is quite fast and would be really fast for a pattern-based solution.
(The above solution for the puzzle in W3 takes a full minute on my old MacBookPro.)

[m_b_metcalf]

Denis,

Thanks for checking them.

I use a rather weird method. The solver uses basic techniques followed by a stage in which each candidate value is tested to see whether it leads to a zero-solution state (I use a fast check for zero solutions; I don't (yet) have a brute force solver for PDs). I make three passes through the solver at each iteration: the first for the puzzle as a standard X-Latin-square, the second on the puzzle transformed so as to make the left diagonals appear as columns, the third so as to make the right diagonals appear as columns.

The next step is to make a brute-force solver.

In the meantime, below is a puzzle based on your solution grid that takes 33s.

Regards,

Mike

Code: Select all

0000000000000001008000000000000200000D0000000060001000000000000080000000000000000000000000C90000060000BA000004A00000000003000000000000B00000000A00009000000007000000B0000  20 clues, 33s

[Mathimagics]

They are at or close to minimality

Hello Mike,

Since you've been away, here's an overview of what I can say about minimal puzzles for order 13 PLS:

• most puzzles are reducible to 13-clues, and many to 12-clues (examples for your 2nd puzzle are given below)

• conventional solvers require some form of T&E (or DFS as I prefer to call it) to solve these, and that takes a very long time for puzzles with less than say 17 clues. That means minimality testing is not generally feasible.

• I am able to do it because I have a bespoke solver (see description here and following posts)

• A search to find a "maximal minimal puzzle" has so far not found any minimal puzzle with more than 15 clues

Cheers
MM

Code: Select all

..............3........................................................C............6..........8...5..D......7...A.......................12...............9.......B......
..............3...................C.................................................6..........8...5..D......7...A.......................12...............9.......B......

[m_b_metcalf]

They are at or close to minimality

Since you've been away, here's an overview of what I can say about minimal puzzles for order 13 PLS:

Mathimagics, Many thanks for bringing me fully up-to-date. My target now is to solve those two puzzles. If, and when, I succeed, I'll let you know!

Regards,

mike

[denis_berthier]

In the meantime, below is a puzzle based on your solution grid that takes 33s

Code: Select all

0000000000000001008000000000000200000D0000000060001000000000000080000000000000000000000000C90000060000BA000004A00000000003000000000000B00000000A00009000000007000000B0000  20 clues, 33s

I checked: it is also in T&E(1).

[denis_berthier]

conventional solvers require some form of T&E (or DFS as I prefer to call it)

This is far from the topic of this thread, but in order to avoid any confusion, I have to correct this.
It is true that DFS is what conventional solvers (including SAT solvers) do. DFS goes as deep as possible in its search and, when backtracking, it always stays as deep as possible.
DFS is generally much faster than T&E but it is unable to produce any readable output.

T&E has nothing to do with DFS.
T&E(1) does exactly the opposite: it stays at depth 1. More generally, T&E(n) never goes deeper than n. It's much closer to BFS than to DFS (though it's not the same procedure either).

In both cases, depth is the cumulated number of simultaneous hypotheses.

[Mathimagics]

Ok, got it, thanks for the clarification!