## Structure of the puzzle solution 1 : the Megaclue !

Everything about Sudoku that doesn't fit in one of the other sections

### Re: Structure of the puzzle solution 1 : the Megaclue !

Code: Select all
`... 4.. .....6 ... .2.8.. ..1 ..5..1 6.. ...... ... .7..7. .2. ...34. ..7 ....8. ... 3..... ... .6. #valid 17-clue puzzle from Gordon's list`

Code: Select all
`... 4.. .....6 ... .2.8.. ..1 ..5..1 6.. ...... ... .7..7. .2. ...3.. ..7 ....8. ... 3..... ... .6. #4 @r7c2 removed = 12 040 692 solutions`

Code: Select all
`... 4.. ...... ... .2.8.. ..1 ..5..1 6.. ...... ... .7..7. .2. ...34. ..7 ....8. ... 3..... ... .6. #6 @r2c3 removed = 13 008 797 solutions`

This is the list of 16-clue pseudo-puzzles with > 10 000 000 solutions obtained by single clue removal from Gordon's list of 49151 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`
dobrichev
2016 Supporter

Posts: 1816
Joined: 24 May 2010

### re: Megaclue

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?

Pat

Posts: 3925
Joined: 18 July 2005

### Re: re: Megaclue

Pat wrote:for the highest previously-reported (11339281),
there was a minimal unavoidable of size 55;
has this now been exceeded?

Wasn't it exceeded already 4 years ago?

RW
RW
2010 Supporter

Posts: 1010
Joined: 16 March 2006

### re: Megaclue

RW wrote:Wasn't it exceeded already 4 years ago?

right, Ocean found a minimal unavoidable of size 60

my question is,
might there be some new discovery in the newer 17s ?

Pat

Posts: 3925
Joined: 18 July 2005

### Re: re: Megaclue

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 puzzle16-clue pseudopuzzles                                                                #Sol   #UA  minUA maxUA000000000006000020800001005001600000000000070070020000340007000080000300000000060    844510  4546   4   45000400000000000020800001005001600000000000070070020000340007000080000300000000060  13008797 12217   4   50000400000006000000800001005001600000000000070070020000340007000080000300000000060    952548  8145   4   46000400000006000020000001005001600000000000070070020000340007000080000300000000060    211019  2422   6   45000400000006000020800000005001600000000000070070020000340007000080000300000000060   1336981 11715   4   49000400000006000020800001000001600000000000070070020000340007000080000300000000060    348474  4241   6   47000400000006000020800001005000600000000000070070020000340007000080000300000000060    109223   342   4   38000400000006000020800001005001000000000000070070020000340007000080000300000000060   4861490  8964   4   50000400000006000020800001005001600000000000000070020000340007000080000300000000060    549168   764   4   44000400000006000020800001005001600000000000070000020000340007000080000300000000060    923010  1645   4   44000400000006000020800001005001600000000000070070000000340007000080000300000000060   1312227  3689   4   49000400000006000020800001005001600000000000070070020000040007000080000300000000060   2763004 15070   6   50000400000006000020800001005001600000000000070070020000300007000080000300000000060  12040692  8614   4   49000400000006000020800001005001600000000000070070020000340000000080000300000000060   3815177 11019   4   53000400000006000020800001005001600000000000070070020000340007000000000300000000060    207206   402   4   43000400000006000020800001005001600000000000070070020000340007000080000000000000060      4265    21   4   25000400000006000020800001005001600000000000070070020000340007000080000300000000000   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}
dobrichev
2016 Supporter

Posts: 1816
Joined: 24 May 2010

### Re: Structure of the puzzle solution 1 : the Megaclue !

Great work - to have the forsight to check the increasingly distant 17s...... they would ,of course, have bigger "megaclues"

Its nice to have an old thread reopened .....

and good to have new people furthuring our understanding of the numbers.

I might open "structure of the puzzle solution 2" soon !

C
coloin

Posts: 2114
Joined: 05 May 2005
Location: Tenerife

### Re: Structure of the puzzle solution 1 : the Megaclue !

BTW the above results are incorrect. The number of solutions is OK, but since the UA set is a property of the solution grid and not of the puzzle:
- the number of UA depends of the grid chosen as basic. In our case the first solution returned by the solver was used for UA generation.
- the UA sizes depend on the UA found and are also grid dependent.
dobrichev
2016 Supporter

Posts: 1816
Joined: 24 May 2010

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