## Thirty Six Clue Puzzle

Post puzzles for others to solve here.

### Thirty Six Clue Puzzle

Code: Select all
`*-----------*|...|7.1|94.||97.|684|1.3||1..|93.|7.6||---+---+---||...|...|...||...|8..|43.||5..|4.3|...||---+---+---||...|1.6|39.||.9.|348|2.1||.1.|.9.|.64|*-----------*`

...7.194.97.6841.31..93.7.6............8..43.5..4.3......1.639..9.3482.1.1..9..64

Australia's new favourite number - 36. Solve it one move Leren
Leren

Posts: 4006
Joined: 03 June 2012

### Re: Thirty Six Clue Puzzle

Gurth's symmetry placement: Need rearrange cols to 546321978 => r4c3<>134789,r7c9<>78
Candidate's mapping in Diagonal: 1<=>3 2<=>2 4<=>9 5<=>5 6<=>6 7<=>8;stte
yzfwsf

Posts: 307
Joined: 16 April 2019

### Re: Thirty Six Clue Puzzle

yzfwsf wrote:Gurth's symmetry placement: Need rearrange cols to 546321978

Who do you think can guess there is a symmetry here, without a solver that tries all the possible morphs?
denis_berthier
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Location: Paris

### Re: Thirty Six Clue Puzzle

denis_berthier wrote:Who do you think can guess there is a symmetry here, without a solver that tries all the possible morphs?

I am not good at solving manually, this is just the solution path output by my computer program. But I’m sure that at least eleven can perform the same step manually.
yzfwsf

Posts: 307
Joined: 16 April 2019

### Re: Thirty Six Clue Puzzle

Leren wrote:...7.194.97.6841.31..93.7.6............8..43.5..4.3......1.639..9.3482.1.1..9..64
Australia's new favourite number - 36. Solve it one move Leren

Interesting! 36 givens is extremely rare for minimal puzzles. Is this one minimal?

As for a solution in one move, I'm far from it - without using an impossible to find symmetry.
What's noticeable in this resolution path is, even with whips activated, none appears (apart from the trivial whips[1]): reversible chains are enough. At this point, I can't say if this has anything to do with symmetry.

Hidden Text: Show
***********************************************************************************************
*** SudoRules 20.1.s based on CSP-Rules 2.1.s, config = W+SFin
*** Using CLIPS 6.32-r779
***********************************************************************************************
x-wing-in-columns: n5{c4 c7}{r4 r9} ==> r9c6 ≠ 5, r9c3 ≠ 5, r4c9 ≠ 5, r4c8 ≠ 5, r4c6 ≠ 5, r4c5 ≠ 5
x-wing-in-rows: n5{r2 r8}{c3 c8} ==> r7c3 ≠ 5, r3c8 ≠ 5, r3c3 ≠ 5, r1c3 ≠ 5
biv-chain[3]: r1c5{n2 n5} - b3n5{r1c9 r2c8} - r2n2{c8 c3} ==> r1c1 ≠ 2, r1c2 ≠ 2, r1c3 ≠ 2
biv-chain[3]: r1c5{n2 n5} - b8n5{r7c5 r9c4} - c4n2{r9 r4} ==> r4c5 ≠ 2, r5c5 ≠ 2, r6c5 ≠ 2
z-chain-bn[3]: b5n2{r4c6 r5c6} - b2n2{r3c6 r1c5} - b3n2{r1c9 .} ==> r4c8 ≠ 2
z-chain-bn[3]: b1n2{r3c3 r3c2} - b2n2{r3c6 r1c5} - b8n2{r7c5 .} ==> r9c3 ≠ 2
z-chain-rc[3]: r6c7{n6 n8} - r6c2{n8 n2} - r5c2{n2 .} ==> r6c3 ≠ 6
z-chain-rc[3]: r8c1{n6 n7} - r5c1{n7 n2} - r5c2{n2 .} ==> r4c1 ≠ 6
biv-chain[4]: r2c3{n2 n5} - b3n5{r2c8 r1c9} - b6n5{r5c9 r4c7} - r4c4{n5 n2} ==> r4c3 ≠ 2
z-chain[5]: c6n5{r5 r3} - r1c5{n5 n2} - r1c9{n2 n8} - b9n8{r7c9 r9c7} - c7n5{r9 .} ==> r5c9 ≠ 5
singles ==> r4c7 = 5, r4c4 = 2, r9c4 = 5, r9c7 = 8, r6c7 = 6
biv-chain-rc[3]: r1c5{n5 n2} - r7c5{n2 n7} - r7c9{n7 n5} ==> r1c9 ≠ 5
singles ==> r2c8 = 5, r2c3 = 2, r8c8 = 7, r7c9 = 5, r8c1 = 6, r8c3 = 5
biv-chain[3]: r5c1{n7 n2} - r9n2{c1 c6} - b8n7{r9c6 r7c5} ==> r7c1 ≠ 7, r5c5 ≠ 7
biv-chain[3]: r7n7{c3 c5} - r6c5{n7 n1} - r5n1{c5 c3} ==> r5c3 ≠ 7
biv-chain[3]: b3n8{r1c9 r3c8} - c8n2{r3 r6} - r6c2{n2 n8} ==> r6c9 ≠ 8, r1c2 ≠ 8
biv-chain[3]: c9n8{r4 r1} - r1c1{n8 n3} - c2n3{r1 r4} ==> r4c2 ≠ 8
biv-chain[4]: r6c5{n1 n7} - r7c5{n7 n2} - c6n2{r9 r3} - c8n2{r3 r6} ==> r6c8 ≠ 1
hidden-single-in-a-block ==> r4c8 = 1
naked-pairs-in-a-row: r6{c2 c8}{n2 n8} ==> r6c9 ≠ 2, r6c3 ≠ 8
finned-swordfish-in-rows: n2{r3 r6 r9}{c6 c8 c2} ==> r7c2 ≠ 2
whip[1]: b7n2{r9c1 .} ==> r5c1 ≠ 2
naked-single ==> r5c1 = 7
biv-chain-rc[3]: r6c3{n9 n1} - r6c5{n1 n7} - r4c6{n7 n9} ==> r4c3 ≠ 9
hidden-pairs-in-a-block: b4{r5c3 r6c3}{n1 n9} ==> r5c3 ≠ 6
biv-chain[4]: r9c3{n3 n7} - r7n7{c3 c5} - r4c5{n7 n6} - c3n6{r4 r1} ==> r1c3 ≠ 3
biv-chain[4]: b8n2{r7c5 r9c6} - r9c1{n2 n3} - r1n3{c1 c2} - r1n5{c2 c5} ==> r1c5 ≠ 2
stte

DEFISE, could you try your path optimisation on this puzzle (without using symmetry)?
denis_berthier
2010 Supporter

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Location: Paris

### Re: Thirty Six Clue Puzzle

yzfwsf wrote:
denis_berthier wrote:Who do you think can guess there is a symmetry here, without a solver that tries all the possible morphs?

I am not good at solving manually, this is just the solution path output by my computer program. But I’m sure that at least eleven can perform the same step manually.

Yes, I understand. I can't say for eleven. If he still watches this forum, it'd be interesting to know what he thinks.

However, my question was more: who, without knowing in advance there is a symmetry to be found, would even try to find one?

Knowing in advance there is a symmetry, finding it is a different challenge. For what it's worth, if your solver is able to find all the symmetries, it might be fun to warn the user that there is some symmetry and the challenge is to find it.
denis_berthier
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Posts: 1983
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Location: Paris

### Re: Thirty Six Clue Puzzle

denis_berthier wrote : I can't say for eleven. If he still watches this forum, it'd be interesting to know what he thinks.

Yes eleven has equalled this feat before - manually, and with a similar hint - the low number of moves - see here. Now that was truly awesome.

In any event, I was just crowing after Australia annihilated India in an International (Test) cricket match today, dismissing them for the equal 5th lowest completed innings total (36) in the 2,300 odd matches that have been played since 1877.

Leren
Leren

Posts: 4006
Joined: 03 June 2012

### Re: Thirty Six Clue Puzzle

Leren wrote:
denis_berthier wrote : I can't say for eleven. If he still watches this forum, it'd be interesting to know what he thinks.

Yes eleven has equalled this feat before - manually, and with a similar hint - the low number of moves - see here. Now that was truly awesome.

Great, for sure. But what (except maybe eleven) if no hint at all was given? Useful symmetries are statistically extremely rare (except here where they have become fashionable); they may take much time to find if far from their obvious form; as a result, I don't think they can belong to the usual toolkit. That's why I suggested giving a hint in yzf... solver if they are not in their direct form (or close to it).
denis_berthier
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Location: Paris

### Re: Thirty Six Clue Puzzle

denis_berthier wrote:z-chain[5]: c6n5{r5 r3} - r1c5{n5 n2} - r1c9{n2 n8} - b9n8{r7c9 r9c7} - c7n5{r9 .} ==> r5c9 ≠ 5

Your chain symbol will hide the details. I have the same chain in my solver, which looks very complicated.
cfc.PNG (33.14 KiB) Viewed 161 times

Cell Forcing Chain: Each candidate in r1c9 true in turn will all lead r5c9<>5
2r1c9 - r1c5 = (2-5)r3c6 = r5c6 - 5r5c9
5r1c9 - 5r5c9
8r1c9 - r7c9 = (8-5)r9c7 = r4c7 - 5r5c9
yzfwsf

Posts: 307
Joined: 16 April 2019

### Re: Thirty Six Clue Puzzle

denis_berthier wrote:Interesting! 36 givens is extremely rare for minimal puzzles. Is this one minimal?

Yes, it's minimal. That was the first thing I checked.
RSW

Posts: 84
Joined: 01 December 2018

### Re: Thirty Six Clue Puzzle

yzfwsf wrote:
denis_berthier wrote:z-chain[5]: c6n5{r5 r3} - r1c5{n5 n2} - r1c9{n2 n8} - b9n8{r7c9 r9c7} - c7n5{r9 .} ==> r5c9 ≠ 5

Your chain symbol will hide the details. I have the same chain in my solver, which looks very complicated.
cfc.PNG

Cell Forcing Chain: Each candidate in r1c9 true in turn will all lead r5c9<>5
2r1c9 - r1c5 = (2-5)r3c6 = r5c6 - 5r5c9
5r1c9 - 5r5c9
8r1c9 - r7c9 = (8-5)r9c7 = r4c7 - 5r5c9

This is not at all the "same" thing.
What you have is a forcing net, starting from 3 possible values in r1c9.
What I have is, in essence, a (3D-)bivalue-chain (or basic AIC) and it can be drawn as such on the grid, following the order of the 2D-cells in my notation. The z-candidates are not "hidden", they are merely not part of the z-chain.
Of course, they are taken into account when the chain progresses within the next 2D-cell, but this is done once and for all and they are totally useless for the next parts of the chain. That's why they can be abstracted.

From a mathematical point of view, you use reasoning by cases from the start and you have to consider 3 streams of reasoning. At any time in a z-chain, I consider a unique stream of reasoning.
denis_berthier
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Location: Paris

### Re: Thirty Six Clue Puzzle

Leren wrote:I was just crowing after Australia annihilated India in an International (Test) cricket match today, dismissing them for the equal 5th lowest completed innings total (36) in the 2,300 odd matches that have been played since 1877.

I saw every ball! It was the most amazing thing ...

Denis - dobrichev has a very large collection of minimal 36 clue puzzles ...

Mathimagics
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### Re: Thirty Six Clue Puzzle

Mathimagics wrote:Denis - dobrichev has a very large collection of minimal 36 clue puzzles ...

What is very large, compared to the full set of minimal puzzles? In unbiased stats, 36-clue has probability close to 0 (indeed so low that it can't be estimated).
denis_berthier
2010 Supporter

Posts: 1983
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Location: Paris

### Re: Thirty Six Clue Puzzle

denis_berthier wrote:DEFISE, could you try your path optimisation on this puzzle (without using symmetry)?

No problem:
My "Simplest first program" => 29 whips[<=5]
My "Few Steps" program => 5 whips[<=5]
Hidden Text: Show
XWing: r2-r8-n5-p38 => -5r1c3 -5r3c3 -5r3c8 -5r4c8 -5r7c3 -5r9c3
XWing: c4-c7-n5-p49 => -5r4c5 -5r4c6 -5r4c9 -5r9c6
whip[5]: r9c7{n8 n5}- b6n5{r4c7 r5c9}- r1c9{n5 n2}- r1c5{n2 n5}- c6n5{r3 .} => -8r7c9
Single: 8r9c7
Single: 6r6c7
Single: 5r4c7
Single: 2r4c4
Single: 5r9c4
whip[3]: r7c5{n7 n2}- r1c5{n2 n5}- c9n5{r1 .} => -7r7c9
Single: 5r7c9
Single: 7r8c8
Single: 6r8c1
Single: 5r8c3
Single: 2r2c3
Single: 5r2c8
whip[5]: r3c8{n8 n2}- r1n2{c9 c5}- r7c5{n2 n7}- r6c5{n7 n1}- r6c8{n1 .} => -8r4c8
Single: 1r4c8
Naked pair: 28-r6c2-r6c8 => -8r6c3 -2r6c9 -8r6c9
whip[3]: c2n2{r5 r7}- c5n2{r7 r1}- c9n2{r1 .} => -2r5c1
Single: 7r5c1
Alignment: 2-c1-b7 => -2r7c2
whip[5]: r3c8{n8 n2}- r1c9{n2 n8}- r1c1{n8 n3}- r9c1{n3 n2}- c6n2{r9 .} => -8r6c8
STTE

Other solution with 2 whips[<=14]
Hidden Text: Show
XWing: r2-r8-n5-p38 => -5r1c3 -5r3c3 -5r3c8 -5r4c8 -5r7c3 -5r9c3
XWing: c4-c7-n5-p49 => -5r4c5 -5r4c6 -5r4c9 -5r9c6
whip[5]: r9c7{n8 n5}- b6n5{r4c7 r5c9}- r1c9{n5 n2}- r1c5{n2 n5}- c6n5{r3 .} => -8r7c9
Single: 8r9c7
Single: 6r6c7
Single: 5r4c7
Single: 2r4c4
Single: 5r9c4
whip[14]: r1c5{n5 n2}- c6n2{r3 r9}- r7c5{n2 n7}- r7c9{n7 n5}- r1c9{n5 n8}- b3n5{r1c9 r2c8}- r8c8{n5 n7}- r8c1{n7 n6}- r1c1{n6 n3}- r9c1{n3 n7}- r5c1{n7 n2}- c9n2{r5 r6}- r6n7{c9 c3}- r6n9{c3 .} => -5r5c5
STTE

N.B: no solution with a single whip or a single braid.
(basic techniques = singles, alignments, naked & hidden pairs, naked triplets , xwing).
DEFISE

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Location: France

### Re: Thirty Six Clue Puzzle

The original puzzle was from my collections of Symmetry puzzles, and was one of Mladen Dorichev's high clue symmetry puzzles, which I assume are all minimal.

I have a collection of his 36 - 38 clue PI and diagonal symmetry puzzles, 463 36's, 90 37's & 12 38's.

Leren
Last edited by Leren on Sun Dec 20, 2020 5:40 am, edited 1 time in total.
Leren

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