## How regular is to generate sudoku with difficulty 9+ SE?

Everything about Sudoku that doesn't fit in one of the other sections
It seems these type of pattern would be started.

Code: Select all
`1.......4.2..8..5...3...6.....ABC....7.DEF.8....GHI.....4...1...5..7..2.6.......3`

change the bottom (1,3,4,6->3,1,6,4)
Finish checking
ABC=123,124,125,126,129

I got some puzzles with 1 solution.
Code: Select all
`1.......4.2..8..5...3...6.....ABC....7.DEF.8....GHI.....4...1...5..7..2.6.......3   1.......4.2..8..5...3...6.....142....7.536.8....798.....4...1...5..7..2.6.......3   9.1 1.......4.2..8..5...3...6.....142....7.536.8....897.....4...1...5..7..2.6.......3   9.1 1.......4.2..8..5...3...6.....142....7.596.8....738.....4...1...5..7..2.6.......3   8.4 1.......4.2..8..5...3...6.....142....7.596.8....837.....4...1...5..7..2.6.......3   8.4 1.......4.2..8..5...3...6.....142....7.635.8....798.....4...1...5..7..2.6.......3   9.0 1.......4.2..8..5...3...6.....142....7.635.8....897.....4...1...5..7..2.6.......3   9.0 1.......4.2..8..5...3...6.....142....7.653.8....798.....4...1...5..7..2.6.......3   8.4 1.......4.2..8..5...3...6.....142....7.653.8....897.....4...1...5..7..2.6.......3   8.4 1.......4.2..8..5...3...6.....142....7.693.8....758.....4...1...5..7..2.6.......3   8.4 1.......4.2..8..5...3...6.....142....7.693.8....857.....4...1...5..7..2.6.......3   8.4 1.......4.2..8..5...3...6.....142....7.695.8....738.....4...1...5..7..2.6.......3   8.4 1.......4.2..8..5...3...6.....142....7.695.8....837.....4...1...5..7..2.6.......3   8.4 1.......4.2..8..5...3...6.....142....7.936.8....758.....4...1...5..7..2.6.......3   9.1 1.......4.2..8..5...3...6.....142....7.936.8....857.....4...1...5..7..2.6.......3   9.1 1.......4.2..8..5...3...6.....142....7.956.8....738.....4...1...5..7..2.6.......3   8.4 1.......4.2..8..5...3...6.....142....7.956.8....837.....4...1...5..7..2.6.......3   8.4 1.......4.2..8..5...3...6.....214....7.365.8....798.....4...1...5..7..2.6.......3   9.1 1.......4.2..8..5...3...6.....214....7.365.8....897.....4...1...5..7..2.6.......3   9.1 1.......4.2..8..5...3...6.....214....7.395.8....768.....4...1...5..7..2.6.......3   8.4 1.......4.2..8..5...3...6.....214....7.395.8....867.....4...1...5..7..2.6.......3   8.4 1.......4.2..8..5...3...6.....214....7.539.8....768.....4...1...5..7..2.6.......3   8.4 1.......4.2..8..5...3...6.....214....7.539.8....867.....4...1...5..7..2.6.......3   8.4 1.......4.2..8..5...3...6.....214....7.935.8....768.....4...1...5..7..2.6.......3   8.4 1.......4.2..8..5...3...6.....214....7.935.8....867.....4...1...5..7..2.6.......3   8.4 1.......4.2..8..5...3...6.....125....7.463.8....798.....4...1...5..7..2.6.......3   9.0 1.......4.2..8..5...3...6.....125....7.463.8....897.....4...1...5..7..2.6.......3   9.0 1.......4.2..8..5...3...6.....125....7.469.8....738.....4...1...5..7..2.6.......3   8.4 1.......4.2..8..5...3...6.....125....7.469.8....837.....4...1...5..7..2.6.......3   8.4 1.......4.2..8..5...3...6.....125....7.693.8....748.....4...1...5..7..2.6.......3   8.4 1.......4.2..8..5...3...6.....125....7.693.8....847.....4...1...5..7..2.6.......3   8.4 1.......4.2..8..5...3...6.....125....7.936.8....748.....4...1...5..7..2.6.......3   9.2 1.......4.2..8..5...3...6.....125....7.936.8....847.....4...1...5..7..2.6.......3   9.2 1.......4.2..8..5...3...6.....125....7.946.8....738.....4...1...5..7..2.6.......3   9.2 1.......4.2..8..5...3...6.....125....7.946.8....837.....4...1...5..7..2.6.......3   9.2 1.......4.2..8..5...3...6.....125....7.964.8....738.....4...1...5..7..2.6.......3   8.9 1.......4.2..8..5...3...6.....125....7.964.8....837.....4...1...5..7..2.6.......3   8.9 1.......4.2..8..5...3...6.....152....7.439.8....768.....4...1...5..7..2.6.......3   8.9 1.......4.2..8..5...3...6.....152....7.439.8....867.....4...1...5..7..2.6.......3   8.9 1.......4.2..8..5...3...6.....152....7.469.8....738.....4...1...5..7..2.6.......3   8.4 1.......4.2..8..5...3...6.....152....7.469.8....837.....4...1...5..7..2.6.......3   8.4 1.......4.2..8..5...3...6.....152....7.693.8....748.....4...1...5..7..2.6.......3   8.4 1.......4.2..8..5...3...6.....152....7.693.8....847.....4...1...5..7..2.6.......3   8.4 1.......4.2..8..5...3...6.....152....7.946.8....738.....4...1...5..7..2.6.......3   9.3 1.......4.2..8..5...3...6.....152....7.946.8....837.....4...1...5..7..2.6.......3   9.3 1.......4.2..8..5...3...6.....152....7.964.8....738.....4...1...5..7..2.6.......3   8.9 1.......4.2..8..5...3...6.....152....7.964.8....837.....4...1...5..7..2.6.......3   8.9 1.......4.2..8..5...3...6.....215....7.346.8....798.....4...1...5..7..2.6.......3   9.0 1.......4.2..8..5...3...6.....215....7.346.8....897.....4...1...5..7..2.6.......3   9.0 1.......4.2..8..5...3...6.....215....7.394.8....768.....4...1...5..7..2.6.......3   9.1 1.......4.2..8..5...3...6.....215....7.394.8....867.....4...1...5..7..2.6.......3   9.1 1.......4.2..8..5...3...6.....215....7.493.8....768.....4...1...5..7..2.6.......3   9.2 1.......4.2..8..5...3...6.....215....7.493.8....867.....4...1...5..7..2.6.......3   9.2 1.......4.2..8..5...3...6.....215....7.943.8....768.....4...1...5..7..2.6.......3   9.2 1.......4.2..8..5...3...6.....215....7.943.8....867.....4...1...5..7..2.6.......3   9.2 1.......4.2..8..5...3...6.....162....7.594.8....738.....4...1...5..7..2.6.......3   8.9 1.......4.2..8..5...3...6.....162....7.594.8....837.....4...1...5..7..2.6.......3   8.9 1.......4.2..8..5...3...6.....216....7.345.8....798.....4...1...5..7..2.6.......3   8.3 1.......4.2..8..5...3...6.....216....7.345.8....897.....4...1...5..7..2.6.......3   8.3 1.......4.2..8..5...3...6.....216....7.349.8....758.....4...1...5..7..2.6.......3   7.3 1.......4.2..8..5...3...6.....216....7.349.8....857.....4...1...5..7..2.6.......3   7.3 1.......4.2..8..5...3...6.....192....7.435.8....768.....4...1...5..7..2.6.......3   8.9 1.......4.2..8..5...3...6.....192....7.435.8....867.....4...1...5..7..2.6.......3   8.9 1.......4.2..8..5...3...6.....219....7.346.8....758.....4...1...5..7..2.6.......3   9.0 1.......4.2..8..5...3...6.....219....7.346.8....857.....4...1...5..7..2.6.......3   9.0 1.......4.2..8..5...3...6.....219....7.534.8....768.....4...1...5..7..2.6.......3   9.2 1.......4.2..8..5...3...6.....219....7.534.8....867.....4...1...5..7..2.6.......3   9.2 `

Note
1.It seems that (G,I)=(7,8)or(8,7) can't change the ER rating.
2.The post isn't finish.

I don't know whether the ER rating will become 10+ or not when continuing taking away some clues.
Hoping continuing.

Code: Select all
`5...1.....4...36....8....9..1...47..7.......2..96...4..6....5....58...3.....2...8`

A puzzle unconcerned with this topic: ER=7.9 but no Forcing Chains.
Last edited by Eioru on Sat Sep 08, 2007 10:58 am, edited 8 times in total.
Eioru

Posts: 182
Joined: 16 August 2006

deleted.
Last edited by JPF on Sat Sep 08, 2007 11:14 am, edited 1 time in total.
JPF
2017 Supporter

Posts: 3766
Joined: 06 December 2005
Location: Paris, France

I suppose a review or recap of what we achieved in this thread would be of some interest.

We have made some of the "hardest" puzzles.

Starting with the 16 clues
note low number of solutions - for the 16 clues -[207008 sol.] [normally 16 clues has 4 million solutions] for your pattern.
Code: Select all
`+---+---+---+|1..|...|..4||.2.|.8.|.5.||..3|...|6..|+---+---+---+|...|...|...||.7.|...|.8.||...|...|...|+---+---+---+|..4|...|1..||.5.|.7.|.2.||6..|...|..3|+---+---+---+`
There is only 2 equivalent ways to put the 7 and the 8 clues in the central box. [reason for your isomorphs above]
The low solution rate is also partly due to the bivalue cells in r1c7,r3c9,r7c1and r9c3 [this might prevent the puzzle from being exceptionally hard !]

We get all the ways to fill in the central box, 5696 ways of which 178 are different [*32]

We then get all the ways we can remove clues from the central box.

The fact that there is a low solution rate for the 16 clues means there will be a lot of different ways to remove clues from a full central box which completes a valid grid. The more puzzles there are the higher the likelihood that we will get a puzzle which is unusually hard to solve. Which is how/why we got hard puzzles like the "Easter Monster".

here are two of the hardest from your template
Code: Select all
`4 clues1.......4.2..8..5...3...6......27....7...4.8....3.......4...1...5..7..2.6.......3 # 17122 FNP C20.m/S2.a/M2.53.1235 clues1.......4.2..8..5...3...6.....7......7.93..8....25......4...1...5..7..2.6.......3 # 48231 FNP C21.m/M2.39.672`

here are the essentially different 178 for completeness !
1.......4.2..8..5...3...6.....759....7.234.8....861.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....759....7.324.8....861.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....751....7.294.8....368.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....751....7.394.8....268.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....758....7.324.8....961.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....751....7.924.8....368.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....751....7.394.8....862.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....751....7.364.8....298.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....751....7.364.8....928.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....357....7.429.8....861.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....517....7.294.8....368.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....817....7.324.8....569.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....217....7.594.8....368.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....357....7.492.8....861.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....517....7.924.8....368.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....917....7.324.8....568.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....817....7.594.8....362.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....957....7.432.8....861.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....857....7.432.8....961.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....357....7.462.8....891.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....397....7.564.8....812.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....597....7.364.8....812.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....937....7.462.8....851.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....567....7.214.8....398.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....827....7.451.8....369.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....827....7.514.8....369.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....267....7.451.8....398.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....897....7.451.8....362.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....897....7.514.8....362.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....567....7.314.8....928.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....967....7.451.8....328.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....967....7.451.8....832.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....735....7.249.8....861.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....729....7.345.8....861.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....721....7.349.8....865.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....791....7.345.8....268.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....792....7.345.8....861.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....795....7.342.8....861.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....791....7.342.8....865.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....791....7.345.8....862.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....735....7.942.8....861.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....765....7.241.8....839.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....769....7.241.8....835.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....765....7.241.8....398.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....798....7.241.8....365.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....217....7.495.8....368.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....817....7.429.8....365.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....817....7.495.8....362.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....817....7.492.8....365.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....561....7.249.8....837.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....861....7.249.8....537.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....561....7.349.8....827.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....861....7.342.8....597.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....561....7.942.8....837.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....861....7.942.8....537.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....819....7.465.8....327.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....815....7.462.8....397.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....812....7.465.8....397.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....567....7.241.8....398.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....827....7.415.8....369.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....827....7.541.8....369.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....267....7.415.8....398.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....267....7.541.8....398.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....897....7.415.8....362.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....897....7.541.8....362.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....967....7.415.8....328.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....897....7.412.8....365.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....967....7.541.8....832.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....768....7.934.8....251.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....768....7.534.8....291.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....764....7.251.8....938.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....748....7.961.8....235.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....761....7.235.8....948.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....764....7.291.8....538.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....748....7.691.8....235.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....761....7.239.8....548.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....765....7.932.8....814.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....768....7.253.8....914.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....768....7.235.8....914.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....718....7.963.8....254.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....758....7.263.8....914.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....768....7.239.8....514.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....718....7.639.8....254.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....968....7.213.8....754.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....218....7.963.8....754.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....812....7.963.8....754.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....618....7.239.8....754.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....218....7.639.8....754.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....812....7.639.8....754.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....619....7.235.8....748.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....618....7.239.8....745.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....615....7.239.8....748.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....968....7.231.8....754.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....648....7.251.8....739.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....648....7.239.8....751.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....648....7.291.8....735.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....648....7.235.8....791.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....256....7.439.8....718.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....816....7.439.8....752.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....764....7.235.8....198.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....798....7.165.8....234.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....746....7.239.8....158.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....764....7.239.8....158.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....758....7.169.8....234.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....748....7.196.8....235.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....746....7.235.8....198.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....756....7.239.8....418.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....768....7.253.8....419.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....758....7.236.8....419.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....758....7.263.8....419.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....816....7.932.8....745.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....916....7.235.8....748.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....168....7.235.8....794.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....248....7.156.8....739.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....168....7.239.8....754.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....912....7.643.8....758.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....512....7.643.8....798.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....528....7.643.8....719.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....698....7.541.8....723.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....698....7.341.8....725.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....968....7.451.8....723.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....568....7.491.8....723.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....658....7.941.8....723.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....658....7.341.8....729.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....652....7.943.8....718.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....692....7.354.8....718.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....628....7.354.8....719.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....652....7.394.8....718.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....658....7.314.8....729.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....628....7.349.8....715.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....628....7.345.8....719.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....628....7.543.8....719.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....692....7.543.8....718.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....618....7.349.8....725.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....618....7.345.8....729.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....618....7.543.8....729.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....765....7.392.8....814.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....798....7.362.8....514.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....768....7.392.8....514.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....719....7.623.8....548.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....812....7.653.8....794.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....892....7.613.8....754.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....928....7.613.8....754.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....618....7.923.8....754.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....812....7.693.8....754.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....852....7.613.8....794.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....852....7.613.8....749.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....618....7.329.8....754.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....618....7.329.8....745.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....618....7.325.8....749.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....618....7.523.8....749.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....615....7.392.8....748.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....428....7.961.8....753.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....428....7.563.8....791.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....928....7.651.8....743.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....428....7.963.8....751.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....428....7.561.8....793.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....528....7.691.8....743.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....726....7.543.8....198.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....726....7.943.8....158.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....928....7.346.8....715.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....168....7.453.8....729.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....168....7.493.8....725.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....756....7.312.8....948.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....796....7.312.8....458.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....796....7.352.8....418.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....756....7.329.8....418.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....756....7.392.8....418.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....756....7.312.8....498.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....718....7.356.8....492.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....798....7.316.8....452.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....718....7.396.8....452.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....758....7.316.8....492.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....756....7.923.8....418.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....765....7.923.8....418.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....715....7.963.8....428.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....928....7.316.8....745.....4...1...5..7..2.6.......3
1.......4.2..8..5...3...6.....916....7.352.8....748.....4...1...5..7..2.6.......3

C
coloin

Posts: 1858
Joined: 05 May 2005

And this one? I doesn't find in this thread.

Code: Select all
`1.......4.A..B..5...3...6.....XXX....B.YYY.A....ZZZ.....6...3...5..A..B.4.......1`

Puzzles discovered. A=9 B=7, Always 2xJellyfish
Code: Select all
`1.......4.9..7..5...3...6.....125....7.463.9....789.....6...3...5..9..7.4.......1   8.4 1.......4.9..7..5...3...6.....125....7.483.9....769.....6...3...5..9..7.4.......1   7.5 1.......4.9..7..5...3...6.....125....7.643.9....789.....6...3...5..9..7.4.......1   7.5 1.......4.9..7..5...3...6.....125....7.683.9....749.....6...3...5..9..7.4.......1   7.3 1.......4.9..7..5...3...6.....142....7.685.9....739.....6...3...5..9..7.4.......1   8.4 1.......4.9..7..5...3...6.....152....7.638.9....749.....6...3...5..9..7.4.......1   7.2 1.......4.9..7..5...3...6.....162....7.543.9....789.....6...3...5..9..7.4.......1   9.0 1.......4.9..7..5...3...6.....214....7.835.9....769.....6...3...5..9..7.4.......1   7.2 `

Note
First serch, ZZZ=7Z9, XXX=(1,2,3)(1,2,4)(1,2,5)(1,2,6)(1,2,8), 8 puzzles.
R6C4 and R6C6 can change position with same ER rating.
Eioru

Posts: 182
Joined: 16 August 2006

Yes there are many templates

I dont think we systematically explored them all !!!!

The hardest puzzles came from 16-subpuzzle templates with around 400000-800000 solutions.

The diagonal clues can be row swapped - there are two different patterns.
Code: Select all
`a.......a.a..B..a...a...a.....XXX....B.XXX.B....XXX.....a...a...a..B..a.a.......ais different froma.......a.a..B..a...a...a.....XXX....B.XXX.B....XXX.....a.....a.a..B..a.a.....a..`

The solitary clues in the boxes 2,4,6 and 8 can be anywhere - but this dramatically influences the solutions for the 16-template. Row swapping moves these clues around.

For every 16 plus 9 grid there are many many puzzles...we only took the hardest 1%, so I am not surprized !

I dont recollect trying your template - with the 25 clues non minimal , the SE tends to increase as you remove clues from the central box.
These 2 puzzles seem to be the best in there
Code: Select all
`1.......4.9..7..5...3...6.....7.6....7.1...9....98......6...3...5..9..7.4.......1 # 44170 FNP C21.m/M2.73.891.......4.9..7..5...3...6......3.....7.1.2.9....985.....6...3...5..9..7.4.......1 # 55146 FNP C22.m/S2.v/M2.139.47`

C
coloin

Posts: 1858
Joined: 05 May 2005

Thanks for spending time searching them.
Again,
Code: Select all
`1.....6.4.2..7..5.3...........XXX....7.XXX.9....XXX...........3.5..9..2.4.6.....11.....6.4.2..7..5.3...........142....7.358.9....769...........3.5..9..2.4.6.....11.....6.4.2..7..5.3...........142....7.368.9....759...........3.5..9..2.4.6.....11.....6.4.2..7..5.3...........142....7.583.9....769...........3.5..9..2.4.6.....11.....6.4.2..7..5.3...........214....7.385.9....769...........3.5..9..2.4.6.....1`

This time is not higher rating then pattern before, but many Swordfish and Aligned Triplet Exclusion when ER=3.8 and 7.5.

Code: Select all
`1.....6.4.2.....5.3...7.......XXX.....7XXX9.....XXX.......9...3.5.....2.4.6.....1`

I can't find one puzzle. No solution or many solutions,
If there exist, please tell me hoe to get it.
Eioru

Posts: 182
Joined: 16 August 2006

Code: Select all
`1.......4.2..8..5...3...6.....7......7.93..8....25......4...1...5..7..2.6.......3 # 48231 FNP C21.m/M2.39.672 # SE 10.5`

Eioru wrote:If there exist, please tell me how to get it.

There appears to be no filling of box five which solves your pattern
I can direct you to programs which do this fairly easily !

C
coloin

Posts: 1858
Joined: 05 May 2005

New 10.0+.

Code: Select all
`7.....4...2.9...5...3.....6.8.1.3........4......769.8.4.....7...5...1.2...6.....3 10.07.....4...2.9...5...3.....6.8.12.......8.4......769.8.4.....7...5...1.2...6.....3 10.37.....4...2.9...5...3.....6.8.123......8.4.......69.8.4.....7...5...1.2...6.....3 10.17.....4...2.9...5...3.....6.8.123......854.......69.8.......7...5...1.2...6.....3 10.2`

It takes me 20 minutes each puzzle.
But it's my first time to produce 10.0+ puzzles.
Eioru

Posts: 182
Joined: 16 August 2006

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