## Futoshiki Generation, properties

For fans of Killer Sudoku, Samurai Sudoku and other variants

### Futoshiki Reduction Test #3

This is a reduced version of #1, yet with just 38 clues (vs 43 for the reduced form above), it has a DFS rating of just 4623 (vs over 100,000+).

Code: Select all
` 9  . . . . . . . . . / . . . . . . . > . / . > . . . < < . . / . . < . . . < < . / . . . . . . . . . / . . . < . . . . . / > . . . . . > . . / . . > . . . . . . / < . . . . < < . . // . . . . < . . . . / . . . . < . . . > / . . . . . . . . . / . . > < . . . . < / . . > < > < > > < / . > . < . . > < < / < . . < < < . . . / . . . . . . . > > / . . . . . . . . . //`

Mathimagics
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### Futoshiki Reduction Test #4

Ok, this is my final offering for the day.

Puzzle #1, reduced, and with no chains of 7, 8 or 9. But still unique!

Code: Select all
`12:23:59 Max chain len = 612:23:59 Hints = 4412.24.25 Begin solver12:25:04 NSoln = 1, itns = 251,035, et = 36.827780`

What a stinker! You can imagine how long it took to reduce ...

Here's the specs:

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` 9  . . . . . . . . . / . . . . . . . > . / . > . . < < . . . / . . < . . . < < . / . . . . . . < . . / . . . . . < . . . / > . > . < < > . . / . . > > . . . . . / . . . . . < < . . // . . . . < . . . . / . . > . . . . < > / . < . . . . . . . / < . > < < . . . < / > . > . > < > . < / . . . < . . > < < / . . . < < . . . . / > . . . . > . > > / . . . . . . . . . //`

Mathimagics
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Posts: 682
Joined: 27 May 2015

### Re: Futoshiki Reduction Test #2

Mathimagics wrote:I've anticipated a 1 line format like Kakuro:
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`9 . . . < . . . < . / . < . . . . . . . / . . . . . < < . . / . . < . . . . . . / . < . . . . < . . / . . . < . < . . . / > . > . < . > . . / . . > . . . . . . / . . . . . < < > . // . . > . < . . . . / . . . . < < . . > / . . . . < . . . < / < . > < . . < . < / > . . < > . > . < / < . . < . > . . < / . > . < . . . . . / > . . . . . . > . / . . . . . . . . . // 9 > > > > . > . > . / . . > . > . . . . / . > . . . . . < . / . . < . . . . . . / < < . . < > . . . / . . . . > > > < . / . . . . . > > . . / . < . > . > . . . / . . > . . > . < . // . < . . > < . . . / < . < . . . . . . / < < . . . . . . . / . . . . . . < . . / . . . . . . . < > / . > . > < . . . . / . > . . < . . < . / > > . . . . < . . / . . . . . . . . . //`

My format is different (here again, it was motivated by quick hand copying), but I can easily manage this.
denis_berthier
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Location: Paris

### Re: Futoshiki Reduction Tests #2, 3 and 4

Mathimagics wrote:I've worked on those two examples, and have reduced them to an extremely reduced form. These take DFS = 100K (egad!) visits. I'm not sure I'd like to tackle them by hand!
They still retain a maximal chain, however. You'd think, oh boy, I've got 9 givens straight away, but you'd quickly run out of "must be"'s. Assuming I'm right in assessing the complexity anyway. We'll see what your system makes of them.

The 3 puzzles require at least 2 levels of T&E (in addition, of course, to the ascending chains). So, I agree, not really for human players.
denis_berthier
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Posts: 1258
Joined: 19 June 2007
Location: Paris

### Futoshiki properties

Could you check this one for me?

It's an example I've just got from atk (H4062), which I wanted to compare. Trouble is, my DFS solver must be in a loop since it's just rolled over 1.6 million visits. I've double-checked the spec and it seems to be right. Can you spot anything I have missed?
Code: Select all
` 9  . > > > . > < < . < . . . < . . . . . . < . < . . < . . < . > . > . . . . . . . . . . . . < . > . . > . . . . . > . < < . . . < . > . < . > > . . < . . . . . . . . . . . . . > > < . < < > . . . . . < . . . . < . . . < . . . . . . < . . . . . . . . . . . . . . . > . < . < < . . . . < < < > . > > . < < . > . . . . . . . . .`

Mathimagics
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Posts: 682
Joined: 27 May 2015

### Re: Futoshiki properties

Mathimagics wrote:Could you check this one for me?
It's an example I've just got from atk (H4062), which I wanted to compare. Trouble is, my DFS solver must be in a loop since it's just rolled over 1.6 million visits. I've double-checked the spec and it seems to be right. Can you spot anything I have missed?
Code: Select all
` 9  . > > > . > < < . < . . . < . . . . . . < . < . . < . . < . > . > . . . . . . . . . . . . < . > . . > . . . . . > . < < . . . < . > . < . > > . . < . . . . . . . . . . . . . > > < . < < > . . . . . < . . . . < . . . < . . . . . . < . . . . . . . . . . . . . . . > . < . < < . . . . < < < > . > > . < < . > . . . . . . . . .`

There's a slight difference with the previous 3. Apart from the eliminations directly due to chains, they didn't allow any elimination at depth 1 of T&E.
In the present case, there is one such elimination, by a long whip:
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`whip[12]: r3c9{n7 n8} - r2c9{n8 n9} - r8c9{n9 n6} - r8c8{n8 n5} - r7c8{n7 n4} - r6c8{n6 n3} - r6c9{n5 n2} - r5c9{n4 n1} - r5c8{n1 n2} - r9c8{n2 n1} - r4c8{n1 n6} - r4c7{n2 .} ==> r4c9 ≠ 7`

But the puzzle still requires at least T&E(2).

(The original H4062 is rather easy, in W3)
denis_berthier
2010 Supporter

Posts: 1258
Joined: 19 June 2007
Location: Paris

### Atk: Futoshiki properties

Their numbering system for Futoshiki is a bit weird: for "Hard" I got 3 examples, the first 2 were H9244 and H9342 and were 8x8, and the 3rd was 9x9 but, H4062. Go figure ....

What do you mean by "the original H4062"?

Mathimagics
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Posts: 682
Joined: 27 May 2015

### Problem with H4062

Can you post a solution to H4062? The ATK interface doesn't seem to offer a "show me the solution" button!

I have had my DFS solver running with unlimited iteration limit on it. So far it has clocked up 25 million node visits, but only progressed to a maximum depth of 61 (and 20 minutes later it hit 62), which tells me that something about this puzzle is very different, and my DFS logic is perhaps vulnerable to certain structures ...

Knowing the solution might help!

Mathimagics
2017 Supporter

Posts: 682
Joined: 27 May 2015

### Re: Problem with H4062

Mathimagics wrote:Can you post a solution to H4062? The ATK interface doesn't seem to offer a "show me the solution" button!

I have had my DFS solver running with unlimited iteration limit on it. So far it has clocked up 25 million node visits, but only progressed to a maximum depth of 61 (and 20 minutes later it hit 62), which tells me that something about this puzzle is very different, and my DFS logic is perhaps vulnerable to certain structures ...
Knowing the solution might help!

Here is the full resolution path (raw output of CSP-Rules):
(asc = ascending-chain)

Hidden Text: Show
Code: Select all
`(solve 9"................................................................................." "->>>-><<<---<-----<-<--<-<->->----------<->-->---->-<<--<->-<->>-<------""--<<--<>-<----<--<----->->----->----------<-->-<>-----<<>--<-<<-<-----<>")**************************************************************************************************  FutoRules 2.0.s based on CSP-Rules 2.0.s, config = W+S***  using CLIPS 6.30-r286***********************************************************************************************0 givens, 729 candidatesasc[4]: r9c9<r8c9<r8c8<r8c7<r9c7 ==> r9c9 ≠ 9, r9c9 ≠ 8, r9c9 ≠ 7, r9c9 ≠ 6, r9c7 ≠ 4, r9c7 ≠ 3, r9c7 ≠ 2, r9c7 ≠ 1, r8c9 ≠ 9, r8c9 ≠ 8, r8c9 ≠ 7, r8c9 ≠ 1, r8c8 ≠ 9, r8c8 ≠ 8, r8c8 ≠ 2, r8c8 ≠ 1, r8c7 ≠ 9, r8c7 ≠ 3, r8c7 ≠ 2, r8c7 ≠ 1,asc[4]: r7c9<r8c9<r8c8<r8c7<r9c7 ==> r7c9 ≠ 9, r7c9 ≠ 8, r7c9 ≠ 7, r7c9 ≠ 6,asc[4]: r6c8<r7c8<r8c8<r8c7<r9c7 ==> r7c8 ≠ 9, r7c8 ≠ 8, r7c8 ≠ 7, r7c8 ≠ 1, r6c8 ≠ 9, r6c8 ≠ 8, r6c8 ≠ 7, r6c8 ≠ 6,asc[1]: r4c8<r5c8 ==> r5c8 ≠ 1, r4c8 ≠ 9,asc[3]: r2c8<r1c8<r1c9<r2c9 ==> r2c9 ≠ 3, r2c9 ≠ 2, r2c9 ≠ 1, r2c8 ≠ 9, r2c8 ≠ 8, r2c8 ≠ 7, r1c9 ≠ 9, r1c9 ≠ 2, r1c9 ≠ 1, r1c8 ≠ 9, r1c8 ≠ 8, r1c8 ≠ 1,asc[4]: r2c7<r1c7<r1c8<r1c9<r2c9 ==> r2c9 ≠ 4, r2c7 ≠ 9, r2c7 ≠ 8, r2c7 ≠ 7, r2c7 ≠ 6, r1c9 ≠ 3, r1c8 ≠ 2, r1c7 ≠ 9, r1c7 ≠ 8, r1c7 ≠ 7, r1c7 ≠ 1,asc[2]: r2c7<r1c7<r1c6 ==> r1c6 ≠ 2, r1c6 ≠ 1,asc[2]: r9c4<r8c4<r8c3 ==> r9c4 ≠ 9, r9c4 ≠ 8, r8c4 ≠ 9, r8c4 ≠ 1, r8c3 ≠ 2, r8c3 ≠ 1,asc[3]: r2c3<r3c3<r3c4<r2c4 ==> r3c4 ≠ 9, r3c4 ≠ 2, r3c4 ≠ 1, r3c3 ≠ 9, r3c3 ≠ 8, r3c3 ≠ 1, r2c4 ≠ 3, r2c4 ≠ 2, r2c4 ≠ 1, r2c3 ≠ 9, r2c3 ≠ 8, r2c3 ≠ 7,asc[1]: r7c2<r8c2 ==> r8c2 ≠ 1, r7c2 ≠ 9,asc[2]: r9c1<r8c1<r8c2 ==> r9c1 ≠ 9, r9c1 ≠ 8, r8c2 ≠ 2, r8c1 ≠ 9, r8c1 ≠ 1,asc[2]: r7c1<r8c1<r8c2 ==> r7c1 ≠ 9, r7c1 ≠ 8,asc[2]: r3c1<r4c1<r5c1 ==> r5c1 ≠ 2, r5c1 ≠ 1, r4c1 ≠ 9, r4c1 ≠ 1, r3c1 ≠ 9, r3c1 ≠ 8,asc[2]: r9c2<r9c3<r8c3 ==> r9c3 ≠ 9, r9c3 ≠ 1, r9c2 ≠ 9, r9c2 ≠ 8,asc[2]: r8c5<r8c6<r9c6 ==> r9c6 ≠ 2, r9c6 ≠ 1, r8c6 ≠ 9, r8c6 ≠ 1, r8c5 ≠ 9, r8c5 ≠ 8,asc[2]: r7c5<r7c6<r6c6 ==> r7c6 ≠ 9, r7c6 ≠ 1, r7c5 ≠ 9, r7c5 ≠ 8, r6c6 ≠ 2, r6c6 ≠ 1,asc[4]: r7c5<r7c6<r7c7<r8c7<r9c7 ==> r7c7 ≠ 9, r7c7 ≠ 8, r7c7 ≠ 2, r7c7 ≠ 1, r7c6 ≠ 8, r7c6 ≠ 7, r7c5 ≠ 7, r7c5 ≠ 6,asc[1]: r7c4<r7c3 ==> r7c4 ≠ 9, r7c3 ≠ 1,asc[1]: r6c7<r6c6 ==> r6c7 ≠ 9,asc[1]: r6c4<r6c3 ==> r6c4 ≠ 9, r6c3 ≠ 1,asc[1]: r6c1<r6c2 ==> r6c2 ≠ 1, r6c1 ≠ 9,asc[1]: r4c7<r4c6 ==> r4c7 ≠ 9, r4c6 ≠ 1,asc[1]: r4c5<r4c4 ==> r4c5 ≠ 9, r4c4 ≠ 1,asc[1]: r4c2<r4c3 ==> r4c3 ≠ 1, r4c2 ≠ 9,asc[1]: r3c8<r3c9 ==> r3c9 ≠ 1, r3c8 ≠ 9,asc[2]: r3c5<r3c6<r4c6 ==> r4c6 ≠ 2, r3c6 ≠ 9, r3c6 ≠ 1, r3c5 ≠ 9, r3c5 ≠ 8,asc[1]: r2c5<r2c6 ==> r2c6 ≠ 1, r2c5 ≠ 9,asc[2]: r2c1<r2c2<r3c2 ==> r3c2 ≠ 2, r3c2 ≠ 1, r2c2 ≠ 9, r2c2 ≠ 1, r2c1 ≠ 9, r2c1 ≠ 8,asc[3]: r1c5<r1c4<r1c3<r1c2 ==> r1c5 ≠ 9, r1c5 ≠ 8, r1c5 ≠ 7, r1c4 ≠ 9, r1c4 ≠ 8, r1c4 ≠ 1, r1c3 ≠ 9, r1c3 ≠ 2, r1c3 ≠ 1, r1c2 ≠ 3, r1c2 ≠ 2, r1c2 ≠ 1,hidden-single-in-a-row ==> r8c5 = 1hidden-single-in-a-row ==> r1c1 = 1hidden-single-in-a-column ==> r5c1 = 9hidden-single-in-a-column ==> r9c8 = 9hidden-single-in-a-column ==> r6c5 = 9hidden-single-in-a-column ==> r3c7 = 9hidden-single-in-a-row ==> r3c8 = 1hidden-single-in-a-row ==> r7c3 = 9hidden-single-in-a-row ==> r8c2 = 9hidden-single-in-a-row ==> r1c6 = 9hidden-single-in-a-column ==> r5c6 = 1hidden-single-in-a-column ==> r2c3 = 1str-asc[1]: r1c3<r1c2 ==> r1c3 ≠ 8str-asc[2]: r1c5<r1c4<r1c3 ==> r1c5 ≠ 6str-asc[2]: r1c5<r1c4<r1c3 ==> r1c4 ≠ 7str-asc[2]: r1c5<r1c4<r1c3 ==> r1c4 ≠ 2str-asc[2]: r1c5<r1c4<r1c3 ==> r1c3 ≠ 3str-asc[1]: r1c3<r1c2 ==> r1c2 ≠ 4str-asc[1]: r2c2<r3c2 ==> r2c2 ≠ 8str-asc[1]: r2c1<r2c2 ==> r2c2 ≠ 2str-asc[1]: r2c1<r2c2 ==> r2c1 ≠ 7str-asc[1]: r2c2<r3c2 ==> r3c2 ≠ 3str-asc[1]: r2c5<r2c6 ==> r2c6 ≠ 2str-asc[1]: r2c5<r2c6 ==> r2c5 ≠ 8str-asc[1]: r3c6<r4c6 ==> r3c6 ≠ 8str-asc[1]: r3c5<r3c6 ==> r3c6 ≠ 2str-asc[1]: r3c5<r3c6 ==> r3c5 ≠ 7str-asc[1]: r3c6<r4c6 ==> r4c6 ≠ 3str-asc[1]: r4c2<r4c3 ==> r4c2 ≠ 8str-asc[1]: r4c5<r4c4 ==> r4c4 ≠ 2str-asc[1]: r4c7<r4c6 ==> r4c7 ≠ 8str-asc[1]: r6c1<r6c2 ==> r6c2 ≠ 2str-asc[1]: r6c1<r6c2 ==> r6c1 ≠ 8str-asc[1]: r6c4<r6c3 ==> r6c4 ≠ 8str-asc[1]: r6c7<r6c6 ==> r6c7 ≠ 8str-asc[1]: r8c7<r9c7 ==> r8c7 ≠ 8str-asc[3]: r7c5<r7c6<r7c7<r8c7 ==> r8c7 ≠ 4str-asc[3]: r7c5<r7c6<r7c7<r8c7 ==> r7c7 ≠ 7str-asc[3]: r7c5<r7c6<r7c7<r8c7 ==> r7c7 ≠ 3str-asc[3]: r7c5<r7c6<r7c7<r8c7 ==> r7c6 ≠ 6str-asc[3]: r7c5<r7c6<r7c7<r8c7 ==> r7c6 ≠ 2hidden-single-in-a-column ==> r8c6 = 2str-asc[3]: r7c5<r7c6<r7c7<r8c7 ==> r7c5 ≠ 5str-asc[3]: r7c6<r7c7<r8c7<r9c7 ==> r9c7 ≠ 5str-asc[1]: r7c6<r6c6 ==> r6c6 ≠ 3str-asc[1]: r9c3<r8c3 ==> r9c3 ≠ 8str-asc[1]: r9c2<r9c3 ==> r9c2 ≠ 7str-asc[1]: r3c1<r4c1 ==> r4c1 ≠ 2str-asc[1]: r8c4<r8c3 ==> r8c4 ≠ 8str-asc[1]: r8c4<r8c3 ==> r8c3 ≠ 3str-asc[1]: r9c4<r8c4 ==> r9c4 ≠ 7str-asc[1]: r2c7<r1c7 ==> r1c7 ≠ 2hidden-single-in-a-row ==> r1c5 = 2str-asc[1]: r2c5<r2c6 ==> r2c6 ≠ 3str-asc[1]: r3c5<r3c6 ==> r3c6 ≠ 3str-asc[1]: r3c6<r4c6 ==> r4c6 ≠ 4str-asc[1]: r4c5<r4c4 ==> r4c4 ≠ 3str-asc[1]: r7c5<r7c6 ==> r7c6 ≠ 3hidden-single-in-a-column ==> r9c6 = 3str-asc[3]: r7c6<r7c7<r8c7<r9c7 ==> r9c7 ≠ 6str-asc[3]: r7c6<r7c7<r8c7<r9c7 ==> r8c7 ≠ 5str-asc[3]: r7c6<r7c7<r8c7<r9c7 ==> r7c7 ≠ 4str-asc[1]: r7c6<r6c6 ==> r6c6 ≠ 4str-asc[3]: r1c7<r1c8<r1c9<r2c9 ==> r2c9 ≠ 5str-asc[3]: r1c7<r1c8<r1c9<r2c9 ==> r1c9 ≠ 4str-asc[3]: r1c7<r1c8<r1c9<r2c9 ==> r1c8 ≠ 3str-asc[1]: r4c8<r5c8 ==> r5c8 ≠ 2str-asc[1]: r4c8<r5c8 ==> r4c8 ≠ 8hidden-single-in-a-column ==> r5c8 = 8hidden-single-in-a-column ==> r9c7 = 8hidden-single-in-a-column ==> r4c5 = 8naked-single ==> r4c4 = 9hidden-single-in-a-row ==> r2c9 = 9hidden-single-in-a-column ==> r8c1 = 8hidden-single-in-a-column ==> r6c3 = 8hidden-single-in-a-column ==> r2c6 = 8str-asc[2]: r3c3<r3c4<r2c4 ==> r3c4 ≠ 8hidden-single-in-a-column ==> r7c4 = 8str-asc[2]: r3c3<r3c4<r2c4 ==> r3c4 ≠ 7str-asc[2]: r3c3<r3c4<r2c4 ==> r3c3 ≠ 7str-asc[2]: r3c3<r3c4<r2c4 ==> r3c3 ≠ 6str-asc[1]: r6c1<r6c2 ==> r6c1 ≠ 7str-asc[1]: r6c7<r6c6 ==> r6c7 ≠ 7str-asc[2]: r9c2<r9c3<r8c3 ==> r9c3 ≠ 7str-asc[2]: r9c2<r9c3<r8c3 ==> r9c2 ≠ 6str-asc[2]: r9c4<r8c4<r8c3 ==> r9c4 ≠ 6str-asc[2]: r9c4<r8c4<r8c3 ==> r8c4 ≠ 7str-asc[1]: r3c1<r4c1 ==> r3c1 ≠ 7str-asc[1]: r4c2<r4c3 ==> r4c2 ≠ 7str-asc[1]: r4c7<r4c6 ==> r4c7 ≠ 7str-asc[2]: r3c5<r3c6<r4c6 ==> r3c6 ≠ 7str-asc[2]: r3c5<r3c6<r4c6 ==> r3c5 ≠ 6str-asc[1]: r8c8<r8c7 ==> r8c8 ≠ 7str-asc[2]: r6c8<r7c8<r8c8 ==> r8c8 ≠ 3str-asc[2]: r6c8<r7c8<r8c8 ==> r7c8 ≠ 6str-asc[2]: r6c8<r7c8<r8c8 ==> r7c8 ≠ 2str-asc[2]: r6c8<r7c8<r8c8 ==> r6c8 ≠ 5str-asc[2]: r8c9<r8c8<r8c7 ==> r8c9 ≠ 6str-asc[1]: r7c9<r8c9 ==> r7c9 ≠ 5str-asc[3]: r9c9<r8c9<r8c8<r8c7 ==> r9c9 ≠ 5515 candidates, 1577 csp-links and 3420 links. Density = 2.58%hidden-pairs-in-a-row: r3{n7 n8}{c2 c9} ==> r3c9 ≠ 6hidden-pairs-in-a-row: r3{n7 n8}{c2 c9} ==> r3c9 ≠ 5hidden-pairs-in-a-row: r3{n7 n8}{c2 c9} ==> r3c9 ≠ 4hidden-pairs-in-a-row: r3{n7 n8}{c2 c9} ==> r3c9 ≠ 3hidden-pairs-in-a-row: r3{n7 n8}{c2 c9} ==> r3c9 ≠ 2hidden-pairs-in-a-row: r3{n7 n8}{c2 c9} ==> r3c2 ≠ 6hidden-pairs-in-a-row: r3{n7 n8}{c2 c9} ==> r3c2 ≠ 5hidden-pairs-in-a-row: r3{n7 n8}{c2 c9} ==> r3c2 ≠ 4whip[2]: r8c7{n6 n7} - r8c3{n7 .} ==> r8c4 ≠ 6str-asc[1]: r9c4<r8c4 ==> r9c4 ≠ 5whip[2]: r7c6{n5 n4} - r3c6{n4 .} ==> r4c6 ≠ 5whip[2]: r4c6{n6 n7} - r4c3{n7 .} ==> r4c2 ≠ 6whip[2]: r7c7{n5 n6} - r1c7{n6 .} ==> r2c7 ≠ 5naked-triplets-in-a-row: r7{c5 c6 c8}{n3 n4 n5} ==> r7c9 ≠ 4naked-triplets-in-a-row: r7{c5 c6 c8}{n3 n4 n5} ==> r7c9 ≠ 3naked-triplets-in-a-row: r7{c5 c6 c8}{n3 n4 n5} ==> r7c7 ≠ 5naked-single ==> r7c7 = 6naked-single ==> r8c7 = 7str-asc[2]: r9c2<r9c3<r8c3 ==> r9c3 ≠ 6str-asc[2]: r9c2<r9c3<r8c3 ==> r9c2 ≠ 5hidden-pairs-in-a-row: r9{n6 n7}{c1 c5} ==> r9c5 ≠ 5hidden-pairs-in-a-row: r9{n6 n7}{c1 c5} ==> r9c5 ≠ 4hidden-pairs-in-a-row: r9{n6 n7}{c1 c5} ==> r9c1 ≠ 5hidden-single-in-a-row ==> r9c3 = 5naked-single ==> r8c3 = 6str-asc[2]: r6c8<r7c8<r8c8 ==> r7c8 ≠ 5str-asc[2]: r6c8<r7c8<r8c8 ==> r6c8 ≠ 4str-asc[2]: r7c9<r8c9<r8c8 ==> r8c9 ≠ 5str-asc[1]: r9c9<r8c9 ==> r9c9 ≠ 4naked-pairs-in-a-column: c9{r7 r9}{n1 n2} ==> r6c9 ≠ 2naked-pairs-in-a-column: c9{r7 r9}{n1 n2} ==> r6c9 ≠ 1naked-pairs-in-a-column: c9{r7 r9}{n1 n2} ==> r5c9 ≠ 2naked-pairs-in-a-column: c9{r7 r9}{n1 n2} ==> r4c9 ≠ 2naked-pairs-in-a-column: c9{r7 r9}{n1 n2} ==> r4c9 ≠ 1naked-pairs-in-a-row: r7{c5 c8}{n3 n4} ==> r7c6 ≠ 4naked-single ==> r7c6 = 5hidden-single-in-a-column ==> r3c6 = 4naked-single ==> r3c5 = 3naked-single ==> r3c3 = 2naked-single ==> r7c5 = 4naked-single ==> r7c8 = 3naked-single ==> r6c8 = 2str-asc[1]: r2c8<r1c8 ==> r1c8 ≠ 4str-asc[1]: r1c8<r1c9 ==> r1c9 ≠ 5str-asc[1]: r6c1<r6c2 ==> r6c2 ≠ 3str-asc[1]: r3c1<r4c1 ==> r4c1 ≠ 5str-asc[1]: r3c1<r4c1 ==> r4c1 ≠ 4str-asc[1]: r3c1<r4c1 ==> r4c1 ≠ 3str-asc[1]: r3c4<r2c4 ==> r2c4 ≠ 5str-asc[1]: r3c4<r2c4 ==> r2c4 ≠ 4naked-pairs-in-a-row: r4{c1 c6}{n6 n7} ==> r4c9 ≠ 7naked-pairs-in-a-row: r4{c1 c6}{n6 n7} ==> r4c9 ≠ 6naked-pairs-in-a-row: r4{c1 c6}{n6 n7} ==> r4c8 ≠ 7hidden-single-in-a-column ==> r1c8 = 7naked-single ==> r1c3 = 4naked-single ==> r1c4 = 3naked-single ==> r1c7 = 5naked-single ==> r1c9 = 8naked-single ==> r1c2 = 6naked-single ==> r3c9 = 7naked-single ==> r3c2 = 8hidden-single-in-a-row ==> r8c9 = 3naked-pairs-in-a-row: r4{c1 c6}{n6 n7} ==> r4c8 ≠ 6hidden-single-in-a-column ==> r2c8 = 6naked-single ==> r2c4 = 7naked-single ==> r2c5 = 5str-asc[1]: r2c1<r2c2 ==> r2c1 ≠ 4naked-pairs-in-a-row: r4{c8 c9}{n4 n5} ==> r4c7 ≠ 4naked-pairs-in-a-row: r4{c8 c9}{n4 n5} ==> r4c2 ≠ 5naked-pairs-in-a-row: r4{c8 c9}{n4 n5} ==> r4c2 ≠ 4naked-pairs-in-a-row: r4{c1 c6}{n6 n7} ==> r4c3 ≠ 7naked-single ==> r4c3 = 3naked-single ==> r5c3 = 7naked-single ==> r5c5 = 6naked-single ==> r9c5 = 7hidden-single-in-a-column ==> r6c9 = 6naked-single ==> r6c6 = 7naked-single ==> r4c6 = 6naked-single ==> r4c1 = 7naked-single ==> r7c1 = 2naked-single ==> r2c1 = 3naked-single ==> r2c2 = 4naked-single ==> r2c7 = 2naked-single ==> r4c7 = 1naked-single ==> r4c2 = 2naked-single ==> r9c2 = 1naked-single ==> r7c2 = 7naked-single ==> r9c9 = 2naked-single ==> r9c4 = 4naked-single ==> r8c4 = 5naked-single ==> r3c4 = 6naked-single ==> r3c1 = 5naked-single ==> r6c1 = 4naked-single ==> r6c7 = 3naked-single ==> r5c7 = 4naked-single ==> r5c9 = 5naked-single ==> r4c9 = 4naked-single ==> r4c8 = 5naked-single ==> r5c2 = 3naked-single ==> r5c4 = 2naked-single ==> r6c4 = 1naked-single ==> r8c8 = 4naked-single ==> r9c1 = 6naked-single ==> r6c2 = 5naked-single ==> r7c9 = 1164329578341758269582634917723986154937261485458197326279845631896512743615473892`
denis_berthier
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### Re: Atk: Futoshiki properties

Mathimagics wrote:Their numbering system for Futoshiki is a bit weird: for "Hard" I got 3 examples, the first 2 were H9244 and H9342 and were 8x8, and the 3rd was 9x9 but, H4062.

They seem to have the same system for all their games: you can't choose size.

Mathimagics wrote:What do you mean by "the original H4062"?
The puzzle on their website, before you dealt with it.
denis_berthier
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### Problem with H4062

denis_berthier wrote:The puzzle on their website, before you dealt with it.

Hmmm, that's just it, I didn't fiddle with it at all. I just wanted to see how it compared with my reduced examples.

I wanted you to check it to see whether I had made any silly mistakes in transcribing it.

Looks like I definitely have a bug ... my DFS has gone crazy!

PS: Thanks for that solver info!

Mathimagics
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### Re: Problem with H4062

Mathimagics wrote:I wanted you to check it to see whether I had made any silly mistakes in transcribing it.
Looks like I definitely have a bug ... my DFS has gone crazy!

I just checked if it couldn't be due to one of the rare cases of a Triplet that is not subsumed by whips[3]. But no. If Subsets are de-activated, the Triplet eliminations in the above path can be obtained by the following sequence:

Code: Select all
`whip[3]: r9c2{n5 n1} - r9c9{n1 n4} - r9c4{n4 .} ==> r9c3 ≠ 2str-asc[1]: r9c3<r8c3 ==> r8c3 ≠ 4whip[2]: r8n3{c9 c4} - r8n4{c4 .} ==> r8c9 ≠ 5str-asc[1]: r7c9<r8c9 ==> r7c9 ≠ 4str-asc[1]: r9c9<r8c9 ==> r9c9 ≠ 4whip[3]: r7n1{c9 c2} - r7n7{c2 c1} - r7n2{c1 .} ==> r7c9 ≠ 3biv-chain[2]: r7c9{n2 n1} - r9c9{n1 n2} ==> r4c9 ≠ 2biv-chain[2]: r7c9{n2 n1} - r9c9{n1 n2} ==> r5c9 ≠ 2biv-chain[2]: r7c9{n2 n1} - r9c9{n1 n2} ==> r6c9 ≠ 2biv-chain[2]: r9c9{n1 n2} - r7c9{n2 n1} ==> r4c9 ≠ 1biv-chain[2]: r9c9{n1 n2} - r7c9{n2 n1} ==> r6c9 ≠ 1whip[3]: r7c6{n5 n4} - r7c8{n4 n3} - r7c5{n3 .} ==> r7c7 ≠ 5`
denis_berthier
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### Problem with H4062

I'm slightly confused!

So, if I understand correctly, the puzzle I gave you as H4062 gave different results (wrt difficulty) than your "original" version?

Perhaps they altered it in between, removing some hints? If you have the original, can you compare them?

Mathimagics
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### Re: Problem with H4062

Mathimagics wrote:I'm slightly confused!
So, if I understand correctly, the puzzle I gave you as H4062 gave different results (wrt difficulty) than your "original" version?
Perhaps they altered it in between, removing some hints? If you have the original, can you compare them?

I already had H4062 among those I had copied from the atk site. It hasn't changed since that time. And the solution(s) I gave above are for this "real" H4062.

In my format, with only inequalities (8 * 9 lines + 8 * 9 columns), (- means no sign):
horiz = "->>>-><<<---<-----<-<--<-<->->----------<->-->---->-<<--<->-<->>-<------" 1st to last line
verti = "--<<--<>-<----<--<----->->----->----------<-->-<>-----<<>--<-<<-<-----<>" 1st to last column

So the verti part is different from yours (or am I misinterpreting your format?)
Code: Select all
`9  . > > > . > < < . < . . . < . . . . . . < . < . . < . . < . > . > . . . . . . . . . . . . < . > . . > . . . . . > . < < . . . < . > . < . > > . . < . . . . . . . . . . . . . > > < . < < > . . . . . < . . . . < . . . < . . . . . . < . . . . . . . . . . . . . . . > . < . < < . . . . < < < > . > > . < < . > . . . . . . . . .`

I didn't check because I thought you were proposing a puzzle you had created by modifying atk's.
Attachments
H4062.png (87.5 KiB) Viewed 159 times
Last edited by denis_berthier on Tue Jun 16, 2015 2:40 pm, edited 1 time in total.
denis_berthier
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### Re: Problem with H4062

denis_berthier wrote: am I misinterpreting your format?
Code: Select all
`9  . > > > . > < < . < . . . < . . . . . . < . < . . < . . < . > . > . . . . . . . . . . . . < . > . . > . . . . . > . < < . . . < . > . < . > > . . < . . . . . . . . . . . . . > > < . < < > . . . . . < . . . . < . . . < . . . . . . < . . . . . . . . . . . . . . . > . < . < < . . . . < < < > . > > . < < . > . . . . . . . . .`

I got it! Your format is ambiguous: there's one sign too much per line. It is likely that my translation to my format doesn't correspond to what you intended.
denis_berthier
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