urhegyi wrote:My conclusion when starting to solve 2X3 and 2X4 sudokus is that through the symmetry they are less difficult to solve as the 3X3 one's.

I found a post on 2X3 where all different grids were calculated and stated that the maximum difficulty was around SE 8.3.

Is there simular work done on 2X4 and what's the hardest puzzle possible?

the relevant thread is

here. there are nine 6x6 SE 8.4's after singles

- Code: Select all
`1...56...1..21...5.35..13.1.6..62.1.`

....5.4....3...5.1...34.3.2.1..6..3.

.2......61..2.4...61.....4.6.5.6..3.

.2.4....6...2.4...61......2..5..123.

.....64...2.23...1..5..2...61....2.4

1....6....2..3..6.6.5.4....61....2.4

..3....5.1....456...5..234....5.1...

..34...5.....3..6..1.3.234....5.1...

1...5......3...5.1...34...2..556...4

the first one has 16 clues. the other 8 all have 12 clues and the complements of the clue grid in the solution grid are all isomorphic, but i'm not sure if the 8 puzzles are all isomorphic.

come to think of it i only rated about 70% of the 542257 no-first-single 6x6 puzzles because they have a 9x9 representation and i could plug them into champagne's skfr. after two years, i never got around to doing the other 30% of them with 1to9only's 6x6 explainer! i'll get that done at some point in the hope that another 8.4 or harder puzzle will show up

i highly doubt that an exhaustive search of all 8x8 puzzles would be possible as my guess is that the search space would be too big

1to9only wrote:I think 6x6-DG generates some valid grids, but they are all singles only, ED=1.2/1.5 [edit: this is from a small sample. on a much larger sample, about 2% are non-singles only!].

6x6-DG-X is probably not possible, as I've failed so far to generate a solution grid!!

This probably means DG will not make it into Sukaku6Explainer.

no 6x6-DG-X grid exists. i did an exhaustive pencil-and-paper search this morning because of boredom (don't ask)

**boring manual proof of non existence: **Showassume 2Rx3C boxes, and fill in row 1 with 123456

notation: "1/" and "1\" mean a hidden single or locked candidate elimination by looking at the 1s in the "/" and "\" diagonals respectively. "ns" means naked single(s)

split into cases, based on the order of 4,5,6 in r2c123

case r2c123=456:

6\ r34c5-6

6b4 r4c4=6

(*) 14/ r4c2-14

ns r4c2=3

3\ r6c4-3

oddagon 3r2c4,r2c6,r6c6,r6c1,r3c4 => no solution

case r2c123=465:

5\ r4c4=5

same as (*) from above

case r2c123=546:

r4c4=6 as from case 456

5/ r3c3-5

ns r3c3=2, r5c5=3, r5c2=1, no 1 in c3

case r2c123=564:

r3c3=2 as from case 546

4\ r5c5=4

4/ r6c1=4

4b3 r4c2=4

ns r4c4=3, r6c6=5, r3c4=5, no 5 in c2

case r2c1=6:

6\ r5c5=6, no 6 in b4