Pat wrote:dobrichev wrote:This is the list of
16-clue pseudo-puzzles with > 10 000 000 solutions
obtained by single clue removal from Gordon's list of
49,151 17s
- Code: Select all
.................1..2.34..........5....6......7.....34...7...4...6.1....83....2.. 10432440
..............1..2..3.4..5........6..2...7....7..........6..3...8......49...85... 10789663
..............1..2..3....4.......1.5......6...26.4.........6......3.....5..78..9. 11077028
..............1..2..3....4.........5....3.....34.6........7..8..279......5....1.. 11339281
........1.....2.....3.4..5......61...3......67...5.........73...4.......5..8..... 12040692
..............1..2..3..4.5........3....26.....6.............7...8.5..4..41......9 12602377
........1.....2.....3.4..5.........6.27.8.....3....7..........8.8.1.....4....6... 13008797
for the highest previously-reported (11339281),
there was a
minimal unavoidable of size
55;
has this now been exceeded?
I didn't check UA during the solution counting pass.
Here are some statistics on UA for the puzzle generating pseudos with 13M and 12.04M solutions.
- Code: Select all
000400000006000020800001005001600000000000070070020000340007000080000300000000060 #original 17-clue puzzle
16-clue pseudopuzzles #Sol #UA minUA maxUA
000000000006000020800001005001600000000000070070020000340007000080000300000000060 844510 4546 4 45
000400000000000020800001005001600000000000070070020000340007000080000300000000060 13008797 12217 4 50
000400000006000000800001005001600000000000070070020000340007000080000300000000060 952548 8145 4 46
000400000006000020000001005001600000000000070070020000340007000080000300000000060 211019 2422 6 45
000400000006000020800000005001600000000000070070020000340007000080000300000000060 1336981 11715 4 49
000400000006000020800001000001600000000000070070020000340007000080000300000000060 348474 4241 6 47
000400000006000020800001005000600000000000070070020000340007000080000300000000060 109223 342 4 38
000400000006000020800001005001000000000000070070020000340007000080000300000000060 4861490 8964 4 50
000400000006000020800001005001600000000000000070020000340007000080000300000000060 549168 764 4 44
000400000006000020800001005001600000000000070000020000340007000080000300000000060 923010 1645 4 44
000400000006000020800001005001600000000000070070000000340007000080000300000000060 1312227 3689 4 49
000400000006000020800001005001600000000000070070020000040007000080000300000000060 2763004 15070 6 50
000400000006000020800001005001600000000000070070020000300007000080000300000000060 12040692 8614 4 49
000400000006000020800001005001600000000000070070020000340000000080000300000000060 3815177 11019 4 53
000400000006000020800001005001600000000000070070020000340007000000000300000000060 207206 402 4 43
000400000006000020800001005001600000000000070070020000340007000080000000000000060 4265 21 4 25
000400000006000020800001005001600000000000070070020000340007000080000300000000000 5805479 4918 4 50
You see the records for solution count, number of uncovered UA, and large UA belong to 3 different puzzles of this family.
The pseudopuzzle with 3815177 solutions has 2 UA53 and here they are.
{11,12,13,16,18,19,21,22,24,26,27,29,32,33,34,35,37,38,41,42,45,46,47,48,49,51,53,54,55,57,59,61,64,67,68,69,73,74,75,76,78,83,85,86,89,91,92,93,94,95,96,97,99}
{11,12,13,16,18,19,21,22,24,26,27,29,32,33,34,35,37,38,42,45,46,47,48,49,51,53,54,55,57,59,61,64,67,68,69,73,74,75,76,77,78,83,85,86,89,91,92,93,94,95,96,97,99}The pseudopuzzle with 12602377 solutions leaves 9385 UA uncovered. The largest two are of size 52.
{11,12,13,14,16,17,18,19,21,22,23,24,25,27,28,31,32,35,37,39,42,43,45,46,47,49,51,52,56,58,59,61,63,64,65,66,67,68,71,72,75,76,78,79,81,83,85,89,93,94,95,97}
{12,14,15,16,17,18,19,21,22,23,25,27,28,31,35,37,39,41,43,44,45,46,47,49,51,52,56,57,58,59,63,64,65,67,68,72,73,74,75,76,78,79,81,83,85,89,93,94,95,96,97,98}
