The hardest sudokus

Everything about Sudoku that doesn't fit in one of the other sections
Eioru wrote:.....4..7.9..8..2.6..3.......4.....8.5..7..9.1.....6..8....6.......2..5...19..3..
.....9..6.3..2..4.7..8.......3.....5.6..1..2.1.....7..2....5.......6..3...92..8..

Thanks, the first one is a toughie (4 steps), i will add it to my list with Ocean's new puzzles.
The second one may be nice for pencil&paper (a turbot fish solves).
ravel

Posts: 998
Joined: 21 February 2006

Hi Ronk,

Ronk wrote:Before e9=4, don't you need c8=9, a8=6, and g8=4?
not really. Before b7=4, e79=48, so its a naked pair, so if b7=4, e9 automatically is 4. For clearity's reason, I should perhaps have included e7=8 before e9=4. But your question led me to another observation, that the contradiction already occurs one step earlier, so the improved deduction should read like this now:

g5=7, (k1=7, g3=1, d1=1, f4=1, k9=1, c7=1, f3=3, f9=7, d7=3, g9=3, c6=7, d4=7, c2=3, h1=3, k6=3, a4=3, k5=9, e1=2, f2=6, c3=2, gh4=26, df8=2, k8=8, k2=2, d5=8, c5=6, a5=4, b6=9, e4=9, e3=5, a2=5, b9=5, b7=4, e7=8, e9=4, h2=4, column2!=8, contradiction >) g5!=7

Ronk wrote:And when you have naked pair steps like "gh4=26, df8=2", I assume you make exclusions without specific assignments. Is that correct?
right. My notation tries to be as short as possible, so the naked pair gh4=26 implies (trivially, I think) be4!=6, alternatively I could have written the hidden pair be4=89, but that would be perhaps even less obvious for some eyes.
And df8=2 implies (trivial step, too) pointing with gk8!=2.
maria45

Posts: 54
Joined: 23 October 2005

Eioru wrote:I find this
.....4..7.9..8..2.6..3.......4.....8.5..7..9.1.....6..8....6.......2..5...19..3..
.....9..6.3..2..4.7..8.......3.....5.6..1..2.1.....7..2....5.......6..3...92..8..

The first puzzle is interesting and difficult.
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

List updated, the BF step ratings of Ocean's list are:

# M21/D21:
17,8,9,6,9,7,9,12,10,8,12,8,11,14
# M22/D22:
14,6,8,4
# D21:
5,5,5,4,4
# D22:
5,8,6,7,8,7,4,7,4

So the list contains number 1,4,5,7 and 9 in my new hardest list.
ravel

Posts: 998
Joined: 21 February 2006

ravel wrote:List updated, the BF step ratings of Ocean's list are:

# M21/D21:
17,8,9,6,9,7,9,12,10,8,12,8,11,14
# M22/D22:
14,6,8,4
# D21:
5,5,5,4,4
# D22:
5,8,6,7,8,7,4,7,4

So the list contains number 1,4,5,7 and 9 in my new hardest list.

Ravel,

Thanks for analyzing all the puzzles!

A bit weird that a new pattern suddenly became the most common for 12+ puzzles.
Ocean

Posts: 442
Joined: 29 August 2005

A rookie question:
What is "step" represent for?
What main differences between a puzzle with 15 steps and 5 step?
Eioru

Posts: 182
Joined: 16 August 2006

I explained it roughly on top of this thread and more detailed here.
ravel

Posts: 998
Joined: 21 February 2006

I find 100 puzzles with
XOO
OXO
OOX
in boxes but center box is empty

this 25 puzzles are choosed by them

1..4..5...8..5..9...5..7..34.....2...6.....8...7.....98..2..3...1..7..6...6..9..4
1..4..7...7..2..3...6..9..59.....8...2.....4...5.....94..2..6...3..7..9...9..3..8
2..3..4...4..9..5...8..4..13.....7...9.....4...2.....61..5..2...5..8..6...7..6..9
2..4..5...8..9..7...7..6..37.....2...9.....3...1.....53..7..9...1..5..4...6..1..8
2..7..9...1..3..5...8..4..61.....8...5.....9...6.....57..9..2...6..1..7...3..7..8
3..7..6...8..4..1...7..2..81.....4...2.....9...6.....57..6..1...9..3..8...2..5..4
3..8..9...5..6..3...9..1..69.....7...3.....2...1.....45..6..8...7..2..4...2..3..9
3..9..5...7..2..3...8..4..99.....8...2.....7...4.....54..8..7...6..7..5...3..6..1
4..2..5...8..7..3...3..6..19.....4...3.....5...8.....61..6..2...9..4..1...2..8..7
4..2..9...6..3..1...8..5..21.....4...7.....3...5.....86..7..3...2..4..9...4..1..5
4..6..2...8..3..7...3..9..46.....7...1.....8...9.....17..4..8...2..1..5...8..5..6 ~ *
4..8..1...7..1..4...6..5..32.....8...4.....5...9.....73..2..5...2..4..3...1..6..9
5..7..4...9..4..5...3..1..92.....9...1.....7...7.....36..5..2...8..9..4...9..6..8
6..1..3...7..6..8...3..4..22.....7...6.....1...4.....59..7..2...2..9..4...5..3..8
6..3..9...5..6..8...1..7..22.....5...6.....3...9.....15..7..4...4..8..9...2..1..8
6..5..9...9..2..1...8..7..25.....3...7.....6...2.....83..2..1...1..4..5...4..8..3
7..1..5...5..2..4...8..5..34.....6...6.....2...1.....93..9..8...4..7..6...9..6..1
7..2..8...2..3..4...8..9..65.....1...1.....9...4.....31..9..5...6..7..8...3..6..4
7..5..3...8..2..6...6..9..12.....7...7.....8...1.....54..8..9...3..4..2...9..3..6
8..5..9...3..2..6...7..8..44.....7...5.....2...1.....61..7..4...9..1..5...3..2..1
8..7..9...3..2..5...4..6..32.....1...4.....9...7.....59..8..6...1..3..7...3..2..4
8..9..3...9..3..4...7..6..59.....2...4.....6...5.....14..8..1...3..5..2...1..7..8 ~ **
9..6..8...6..3..1...7..8..28.....9...3.....5...4.....76..3..7...1..5..2...5..4..1
9..7..8...3..1..5...2..4..68.....9...6.....4...4.....73..4..5...9..6..8...6..1..2
9..8..1...6..5..2...8..9..41.....2...5.....3...4.....68..9..5...9..6..7...3..4..1

* ~ this is specil and has 3 X-Wing 2 XYZ-Wing 3 XY-Wing
** ~ this is rare and has 2 Aligned Triplet Exclusions
Eioru

Posts: 182
Joined: 16 August 2006

Thanks,

number 14 and 18 needed 4 steps.
ravel

Posts: 998
Joined: 21 February 2006

These are choosed from another 100 puzzle and be ordered,
and their difficulty are rated 9.0 and 9.1 by Sudoku Explainer
1..2..3...3..4..5...4..6..24.....7...7.....3...1.....58..1..9...6..5..8...9..7..6
1..2..3...4..5..1...6..7..53.....8...2.....4...7.....97..1..6...5..4..7...8..9..3
1..2..3...4..5..1...6..7..83.....5...8.....7...9.....67..6..9...9..1..4...2..3..5
1..2..3...4..5..1...6..7..88.....9...5.....7...9.....32..3..7...7..6..4...8..2..5
1..2..3...4..5..6...3..7..58.....9...9.....7...1.....62..1..6...1..4..9...4..5..7
1..2..3...4..5..6...5..7..89.....7...1.....2...8.....33..5..4...6..2..1...1..8..9
1..2..3...4..5..6...7..6..84.....2...9.....8...1.....73..9..8...6..2..5...4..8..1
1..2..3...4..5..6...7..8..28.....7...3.....4...6.....59..3..4...5..7..2...1..9..8
1..2..3...4..5..6...7..8..99.....2...3.....4...6.....18..6..7...5..4..1...3..2..8

PS...I did't find a puzzle with this parttern rated grater than 9.1 by S.E.
Eioru

Posts: 182
Joined: 16 August 2006

Thanks again,
3 more with 4 steps: lines 5, 6 and 8.
ravel

Posts: 998
Joined: 21 February 2006

ravel wrote:3 more with 4 steps: lines 5, 6 and 8.

I understand your solver to find a solution path with the smallest number of steps, disregarding the complexity of the steps. I would like to examine the step complexity for the relatively simple 4-steppers above, so ...

... would you please post the exc.usion(s) for the 4 steps for each of the above puzzles? Just the rMcN<>D for each step should be sufficient. [edit: OTOH, the technique names might be helpful too.]

TIA, Ron
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

All following exclusions were done with BF steps.
line 5:
r2c9<>1, r3c7<>4, r7c6<>3, r2c3<>8
r3c5<>1, r3c7<>4, r7c6<>3, r2c3<>8
r4c2<>6, r2c9<>1, r1c6<>4, r1c5<>6
r8c3<>6, r2c9<>1, r1c6<>4, r1c5<>6
r8c4<>8, r2c3<>8, r8c6<>2, r1c2<>5
r8c7<>8, r2c9<>1, r8c6<>2, r4c5<>1
r9c2<>8, r2c9<>1, r1c6<>4, r1c5<>6
r9c5<>6, r2c9<>1, r7c2<>7, r2c3<>8
line 6:
r1c3<>7, r3c2<>9, r2c9<>1, r1c2<>9
r2c3<>2, r1c9<>4, r2c9<>1, r8c3<>9
r3c2<>9, r1c3<>7, r2c9<>1, r1c2<>9
r3c7<>2, r1c9<>4, r2c7<>2, r8c3<>9
r4c4<>3, r1c9<>4, r2c9<>1, r1c3<>9
r7c2<>7, r1c9<>4, r2c9<>1, r8c3<>9
line 8:
r1c8<>5, r1c8<>8, r2c3<>9, r2c4<>7
r1c8<>8, r2c3<>9, r1c8<>5, r2c4<>7
r2c3<>8, r2c3<>9, r1c8<>5, r2c4<>7
r2c3<>9, r1c8<>8, r1c8<>5, r2c4<>7
r3c1<>5, r1c8<>8, r2c3<>9, r2c4<>7
r3c4<>1, r2c6<>3, r1c8<>5, r2c4<>7
r5c1<>7, r7c2<>8, r3c2<>6, r2c4<>7
r5c4<>8, r1c8<>8, r2c3<>9, r1c5<>6
r6c7<>8, r2c6<>3, r1c8<>5, r2c4<>7
r7c5<>8, r1c8<>8, r2c3<>9, r1c5<>6
r8c3<>8, r1c8<>8, r2c3<>9, r1c5<>6

Sorry, i have no trace, which techniques were used for the eliminations.
ravel

Posts: 998
Joined: 21 February 2006

ravel wrote:All following exclusions were done with BF steps.
[size=9]line 5:
r2c9<>1, r3c7<>4, r7c6<>3, r2c3<>8

Sorry I didn't think to ask this in the previous post. Obviously both naked single and hidden single placements are not counted as steps. Is anything else not "counted"?

Perhaps you can point me to another thread where your solver has already been discussed. Thanks again, Ron
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

ronk wrote:Obviously both naked single and hidden single placements are not counted as steps. Is anything else not "counted"?

Tuples (pairs to quads), box interactions, x-wings and UR type 1. If you disable all other methods in a solver, you always should get to the grids, where the BF steps are made.