Hello everyone,
I had an idea for a sudoku. I don't know if it's solvable (I think it is). My own solving-skills are not good enough to know for sure. Can someone solve it to be sure?
The rules:
Normal Sudoku rules apply. The thermometers increase from the bulb end. All horizontal and vertical thermometers with 3 or more squares are given. The blue thermometers are the same as the grey ones, but they start within another thermometer. So they are separate from the thermometer they are in.
I'm new to this forum. Tips and tricks for sudoku making (and solving) are welcome.
Can someone solve my first thermo-sudoku?
6 posts
• Page 1 of 1
Can someone solve my first thermo-sudoku?
by gifmenger » Tue Aug 10, 2021 7:10 pm
Last edited by gifmenger on Mon Aug 30, 2021 8:53 pm, edited 1 time in total.
- gifmenger
- Posts: 4
- Joined: 09 August 2021
Re: Can someone solve my first thermo-sudoku?
by denis_berthier » Wed Aug 11, 2021 4:07 am
.
Hi gifmenger
welcome on this forum.
Thermometers are a very bad visual representation of inequality constraints.
A much simpler way to see a thermometer is merely as a set of inequalities between adjacent cells [unless you mean they increase by 1 only?????).
As a result, the game is Futoshiki + block constraints (and this thread should better be in the "other logic games" section.
My Futoshiki solver (a part of my general CSP solver CSP-Rules) doesn't have a variant with block constraints (which could be called Sudoshiki), but I tried it on this puzzle.
asc-chains correspond to the thermometers (except that they can bend)
hills and valleys correspond to taking into account two thermometers meeting at some point.
Both are build automatically (and trivially) from the inequalities.
(solve 9
"................................................................................."
"------<<-->>>>----->><<<<<---->>---->><<-----<<->>--->>---->>->>>>--<<--"
"->>------->><<>>----->>--->>><<->>->>>-->>->>---------<<->>>----->>-----"
)
***********************************************************************************************
*** FutoRules 2.1.s based on CSP-Rules 2.1.s, config = W+S
*** Using CLIPS 6.32-r813
*** Running on MacBookPro Retina Mid-2012 i7 2.7GHz, 16GB 1600MHz DDR3, MacOS 10.15.7
*** Download from: https://github.com/denis-berthier/CSP-Rules-V2.1
***********************************************************************************************
asc[2]: r4c9<r3c9<r2c9 ==> r4c9≠9, r4c9≠8, r3c9≠9, r3c9≠1, r2c9≠2, r2c9≠1
asc[2]: r6c6<r5c6<r4c6 ==> r6c6≠9, r6c6≠8, r5c6≠9, r5c6≠1, r4c6≠2, r4c6≠1
asc[3]: r6c6<r5c6<r5c5<r4c5 ==> r6c6≠7, r5c6≠8, r5c5≠9, r5c5≠2, r5c5≠1, r4c5≠3, r4c5≠2, r4c5≠1
asc[2]: r3c6<r2c6<r1c6 ==> r3c6≠9, r3c6≠8, r2c6≠9, r2c6≠1, r1c6≠2, r1c6≠1
asc[3]: r3c6<r2c6<r2c5<r1c5 ==> r3c6≠7, r2c6≠8, r2c5≠9, r2c5≠2, r2c5≠1, r1c5≠3, r1c5≠2, r1c5≠1
asc[4]: r3c6<r2c6<r2c5<r2c4<r2c3 ==> r3c6≠6, r2c6≠7, r2c5≠8, r2c4≠9, r2c4≠3, r2c4≠2, r2c4≠1, r2c3≠4, r2c3≠3, r2c3≠2, r2c3≠1
asc[3]: r7c5<r6c5<r5c5<r4c5 ==> r7c5≠9, r7c5≠8, r7c5≠7, r6c5≠9, r6c5≠8, r6c5≠1
asc[2]: r6c4<r7c4<r8c4 ==> r8c4≠2, r8c4≠1, r7c4≠9, r7c4≠1, r6c4≠9, r6c4≠8
asc[3]: r6c4<r5c4<r4c4<r3c4 ==> r6c4≠7, r5c4≠9, r5c4≠8, r5c4≠1, r4c4≠9, r4c4≠2, r4c4≠1, r3c4≠3, r3c4≠2, r3c4≠1
asc[2]: r8c3<r7c3<r6c3 ==> r8c3≠9, r8c3≠8, r7c3≠9, r7c3≠1, r6c3≠2, r6c3≠1
asc[3]: r8c3<r7c3<r7c2<r7c1 ==> r8c3≠7, r7c3≠8, r7c2≠9, r7c2≠2, r7c2≠1, r7c1≠3, r7c1≠2, r7c1≠1
asc[3]: r5c2<r6c2<r7c2<r7c1 ==> r6c2≠9, r6c2≠8, r6c2≠1, r5c2≠9, r5c2≠8, r5c2≠7
asc[2]: r5c2<r4c2<r3c2 ==> r4c2≠9, r4c2≠1, r3c2≠2, r3c2≠1
asc[2]: r5c2<r4c2<r4c3 ==> r4c3≠2, r4c3≠1
asc[2]: r4c1<r3c1<r2c1 ==> r4c1≠9, r4c1≠8, r3c1≠9, r3c1≠1, r2c1≠2, r2c1≠1
asc[2]: r9c5<r9c6<r9c7 ==> r9c7≠2, r9c7≠1, r9c6≠9, r9c6≠1, r9c5≠9, r9c5≠8
asc[4]: r9c3<r9c2<r8c2<r7c2<r7c1 ==> r9c3≠9, r9c3≠8, r9c3≠7, r9c3≠6, r9c2≠9, r9c2≠8, r9c2≠7, r9c2≠1, r8c2≠9, r8c2≠8, r8c2≠2, r8c2≠1, r7c2≠3, r7c1≠4
asc[2]: r9c3<r9c2<r9c1 ==> r9c1≠2, r9c1≠1
asc[3]: r8c9<r8c8<r8c7<r9c7 ==> r9c7≠3, r8c9≠9, r8c9≠8, r8c9≠7, r8c8≠9, r8c8≠8, r8c8≠1, r8c7≠9, r8c7≠2, r8c7≠1
asc[2]: r8c6<r8c5<r8c4 ==> r8c6≠9, r8c6≠8, r8c5≠9, r8c5≠1
asc[3]: r7c8<r7c7<r8c7<r9c7 ==> r7c8≠9, r7c8≠8, r7c8≠7, r7c7≠9, r7c7≠8, r7c7≠1
asc[2]: r7c8<r7c7<r7c6 ==> r7c6≠2, r7c6≠1
asc[2]: r6c6<r6c7<r6c8 ==> r6c8≠2, r6c8≠1, r6c7≠9, r6c7≠1
asc[4]: r5c7<r5c8<r4c8<r3c8<r2c8 ==> r5c8≠9, r5c8≠8, r5c8≠7, r5c8≠1, r5c7≠9, r5c7≠8, r5c7≠7, r5c7≠6, r4c8≠9, r4c8≠8, r4c8≠2, r4c8≠1, r3c8≠9, r3c8≠3, r3c8≠2, r3c8≠1, r2c8≠4, r2c8≠3, r2c8≠2, r2c8≠1
asc[5]: r5c7<r5c8<r4c8<r3c8<r3c9<r2c9 ==> r5c8≠6, r5c7≠5, r4c8≠7, r3c9≠4, r3c9≠3, r3c9≠2, r3c8≠8, r2c9≠5, r2c9≠4, r2c9≠3
asc[3]: r5c7<r5c8<r4c8<r4c7 ==> r4c7≠3, r4c7≠2, r4c7≠1
asc[2]: r5c7<r5c8<r5c9 ==> r5c9≠2, r5c9≠1
asc[3]: r4c9<r4c8<r3c8<r2c8 ==> r4c9≠7
asc[4]: r4c9<r4c8<r3c8<r3c9<r2c9 ==> r4c9≠6
asc[3]: r3c6<r3c7<r3c8<r2c8 ==> r3c7≠9, r3c7≠8, r3c7≠1
asc[4]: r3c6<r3c7<r3c8<r3c9<r2c9 ==> r3c7≠7
asc[3]: r3c6<r3c5<r2c5<r1c5 ==> r3c5≠9, r3c5≠8, r3c5≠1
asc[4]: r3c6<r3c5<r2c5<r2c4<r2c3 ==> r3c5≠7
asc[2]: r2c7<r2c6<r1c6 ==> r2c7≠9, r2c7≠8
asc[3]: r2c7<r2c6<r2c5<r1c5 ==> r2c7≠7
asc[4]: r2c7<r2c6<r2c5<r2c4<r2c3 ==> r2c7≠6
asc[2]: r1c7<r1c8<r1c9 ==> r1c9≠2, r1c9≠1, r1c8≠9, r1c8≠1, r1c7≠9, r1c7≠8
valley[5]: r3c4>r4c4>r5c4>r6c4<r7c4<r8c4 ==> r6c4≠6, r6c4≠5
hill[4]: r5c2<r6c2<r7c2>r8c2>r9c2 ==> r7c2≠4
str-asc[1]: r7c2<r7c1 ==> r7c1≠5
valley[4]: r3c2>r4c2>r5c2<r6c2<r7c2 ==> r5c2≠6
valley[5]: r3c4>r3c5>r3c6<r3c7<r3c8<r3c9 ==> r3c6≠5
x-wing-in-columns: n1{c5 c8}{r7 r9} ==> r9c9≠1, r9c4≠1, r9c3≠1, r7c9≠1
str-asc[1]: r9c3<r9c2 ==> r9c2≠2
str-asc[1]: r9c2<r9c1 ==> r9c1≠3
str-asc[1]: r9c2<r8c2 ==> r8c2≠3
whip[2]: r2n1{c7 c2} - r2n2{c2 .} ==> r2c7≠3, r2c7≠4, r2c7≠5
whip[2]: r4n1{c1 c9} - r4n2{c9 .} ==> r4c1≠3, r4c1≠4, r4c1≠5, r4c1≠6, r4c1≠7
whip[4]: r8c7{n8 n3} - r7c7{n7 n2} - r5c7{n2 n1} - r2c7{n1 .} ==> r9c7≠4
whip[4]: r2c5{n6 n7} - r2c4{n7 n8} - r2c9{n8 n9} - r2c3{n9 .} ==> r2c6≠6
g-whip[5]: c4n1{r6 r1} - c4n2{r1 r9} - r7c4{n2 n4+} - c4n3{r7 r4} - r5c4{n3 .} ==> r6c4≠4
whip[3]: r6c7{n8 n2} - r6c6{n6 n1} - r6c4{n1 .} ==> r6c8≠3
whip[7]: r3n1{c6 c3} - r3n2{c3 c1} - r3n3{c1 c2} - r4c2{n8 n2} - r5c2{n5 n1} - r2n1{c2 c7} - r2n2{c7 .} ==> r3c6≠4
whip[3]: r5c6{n7 n2} - r6c6{n6 n1} - r3c6{n1 .} ==> r4c6≠3
g-whip[7]: c7n9{r9 r4} - c7n8{r4 r6} - r8c7{n8 n6-} - c7n7{r8 r1} - r1c8{n6 n8} - r1c9{n7 n9} - c5n9{r1 .} ==> r9c7≠6
g-whip[7]: c7n9{r9 r4} - c7n8{r4 r6} - r8c7{n8 n5-} - c7n7{r8 r1} - r1c8{n6 n8} - r1c9{n7 n9} - c5n9{r1 .} ==> r9c7≠5
g-whip[11]: r7c7{n7 n2} - r2c7{n2 n1} - r5c7{n1 n4} - r5c8{n3 n5} - r4c8{n5 n6} - r3c8{n6 n7} - r3c9{n6 n8} - r2c9{n8 n9} - r2c8{n9 n8} - r1c8{n8 n5-} - r1c7{n7 .} ==> r8c7≠3
Without the block constraints, it doesn't give much; the eliminations done by asc-chains are trivial; I've proven in [PBCS] that they are equivalent to whips[1] (I keep them here for illustration).
But this can give you an idea of the kind of rules used.
I tried to inject the final resolution state into SudoRules (the representations are compatible) in order to take advantage of the block constraints; it allows more eliminations, but it's not enough for a solution. In this puzzle, mixing the two kinds of constraints is necessary.
Hi gifmenger
welcome on this forum.
Thermometers are a very bad visual representation of inequality constraints.
A much simpler way to see a thermometer is merely as a set of inequalities between adjacent cells [unless you mean they increase by 1 only?????).
As a result, the game is Futoshiki + block constraints (and this thread should better be in the "other logic games" section.
My Futoshiki solver (a part of my general CSP solver CSP-Rules) doesn't have a variant with block constraints (which could be called Sudoshiki), but I tried it on this puzzle.
asc-chains correspond to the thermometers (except that they can bend)
hills and valleys correspond to taking into account two thermometers meeting at some point.
Both are build automatically (and trivially) from the inequalities.
(solve 9
"................................................................................."
"------<<-->>>>----->><<<<<---->>---->><<-----<<->>--->>---->>->>>>--<<--"
"->>------->><<>>----->>--->>><<->>->>>-->>->>---------<<->>>----->>-----"
)
***********************************************************************************************
*** FutoRules 2.1.s based on CSP-Rules 2.1.s, config = W+S
*** Using CLIPS 6.32-r813
*** Running on MacBookPro Retina Mid-2012 i7 2.7GHz, 16GB 1600MHz DDR3, MacOS 10.15.7
*** Download from: https://github.com/denis-berthier/CSP-Rules-V2.1
***********************************************************************************************
asc[2]: r4c9<r3c9<r2c9 ==> r4c9≠9, r4c9≠8, r3c9≠9, r3c9≠1, r2c9≠2, r2c9≠1
asc[2]: r6c6<r5c6<r4c6 ==> r6c6≠9, r6c6≠8, r5c6≠9, r5c6≠1, r4c6≠2, r4c6≠1
asc[3]: r6c6<r5c6<r5c5<r4c5 ==> r6c6≠7, r5c6≠8, r5c5≠9, r5c5≠2, r5c5≠1, r4c5≠3, r4c5≠2, r4c5≠1
asc[2]: r3c6<r2c6<r1c6 ==> r3c6≠9, r3c6≠8, r2c6≠9, r2c6≠1, r1c6≠2, r1c6≠1
asc[3]: r3c6<r2c6<r2c5<r1c5 ==> r3c6≠7, r2c6≠8, r2c5≠9, r2c5≠2, r2c5≠1, r1c5≠3, r1c5≠2, r1c5≠1
asc[4]: r3c6<r2c6<r2c5<r2c4<r2c3 ==> r3c6≠6, r2c6≠7, r2c5≠8, r2c4≠9, r2c4≠3, r2c4≠2, r2c4≠1, r2c3≠4, r2c3≠3, r2c3≠2, r2c3≠1
asc[3]: r7c5<r6c5<r5c5<r4c5 ==> r7c5≠9, r7c5≠8, r7c5≠7, r6c5≠9, r6c5≠8, r6c5≠1
asc[2]: r6c4<r7c4<r8c4 ==> r8c4≠2, r8c4≠1, r7c4≠9, r7c4≠1, r6c4≠9, r6c4≠8
asc[3]: r6c4<r5c4<r4c4<r3c4 ==> r6c4≠7, r5c4≠9, r5c4≠8, r5c4≠1, r4c4≠9, r4c4≠2, r4c4≠1, r3c4≠3, r3c4≠2, r3c4≠1
asc[2]: r8c3<r7c3<r6c3 ==> r8c3≠9, r8c3≠8, r7c3≠9, r7c3≠1, r6c3≠2, r6c3≠1
asc[3]: r8c3<r7c3<r7c2<r7c1 ==> r8c3≠7, r7c3≠8, r7c2≠9, r7c2≠2, r7c2≠1, r7c1≠3, r7c1≠2, r7c1≠1
asc[3]: r5c2<r6c2<r7c2<r7c1 ==> r6c2≠9, r6c2≠8, r6c2≠1, r5c2≠9, r5c2≠8, r5c2≠7
asc[2]: r5c2<r4c2<r3c2 ==> r4c2≠9, r4c2≠1, r3c2≠2, r3c2≠1
asc[2]: r5c2<r4c2<r4c3 ==> r4c3≠2, r4c3≠1
asc[2]: r4c1<r3c1<r2c1 ==> r4c1≠9, r4c1≠8, r3c1≠9, r3c1≠1, r2c1≠2, r2c1≠1
asc[2]: r9c5<r9c6<r9c7 ==> r9c7≠2, r9c7≠1, r9c6≠9, r9c6≠1, r9c5≠9, r9c5≠8
asc[4]: r9c3<r9c2<r8c2<r7c2<r7c1 ==> r9c3≠9, r9c3≠8, r9c3≠7, r9c3≠6, r9c2≠9, r9c2≠8, r9c2≠7, r9c2≠1, r8c2≠9, r8c2≠8, r8c2≠2, r8c2≠1, r7c2≠3, r7c1≠4
asc[2]: r9c3<r9c2<r9c1 ==> r9c1≠2, r9c1≠1
asc[3]: r8c9<r8c8<r8c7<r9c7 ==> r9c7≠3, r8c9≠9, r8c9≠8, r8c9≠7, r8c8≠9, r8c8≠8, r8c8≠1, r8c7≠9, r8c7≠2, r8c7≠1
asc[2]: r8c6<r8c5<r8c4 ==> r8c6≠9, r8c6≠8, r8c5≠9, r8c5≠1
asc[3]: r7c8<r7c7<r8c7<r9c7 ==> r7c8≠9, r7c8≠8, r7c8≠7, r7c7≠9, r7c7≠8, r7c7≠1
asc[2]: r7c8<r7c7<r7c6 ==> r7c6≠2, r7c6≠1
asc[2]: r6c6<r6c7<r6c8 ==> r6c8≠2, r6c8≠1, r6c7≠9, r6c7≠1
asc[4]: r5c7<r5c8<r4c8<r3c8<r2c8 ==> r5c8≠9, r5c8≠8, r5c8≠7, r5c8≠1, r5c7≠9, r5c7≠8, r5c7≠7, r5c7≠6, r4c8≠9, r4c8≠8, r4c8≠2, r4c8≠1, r3c8≠9, r3c8≠3, r3c8≠2, r3c8≠1, r2c8≠4, r2c8≠3, r2c8≠2, r2c8≠1
asc[5]: r5c7<r5c8<r4c8<r3c8<r3c9<r2c9 ==> r5c8≠6, r5c7≠5, r4c8≠7, r3c9≠4, r3c9≠3, r3c9≠2, r3c8≠8, r2c9≠5, r2c9≠4, r2c9≠3
asc[3]: r5c7<r5c8<r4c8<r4c7 ==> r4c7≠3, r4c7≠2, r4c7≠1
asc[2]: r5c7<r5c8<r5c9 ==> r5c9≠2, r5c9≠1
asc[3]: r4c9<r4c8<r3c8<r2c8 ==> r4c9≠7
asc[4]: r4c9<r4c8<r3c8<r3c9<r2c9 ==> r4c9≠6
asc[3]: r3c6<r3c7<r3c8<r2c8 ==> r3c7≠9, r3c7≠8, r3c7≠1
asc[4]: r3c6<r3c7<r3c8<r3c9<r2c9 ==> r3c7≠7
asc[3]: r3c6<r3c5<r2c5<r1c5 ==> r3c5≠9, r3c5≠8, r3c5≠1
asc[4]: r3c6<r3c5<r2c5<r2c4<r2c3 ==> r3c5≠7
asc[2]: r2c7<r2c6<r1c6 ==> r2c7≠9, r2c7≠8
asc[3]: r2c7<r2c6<r2c5<r1c5 ==> r2c7≠7
asc[4]: r2c7<r2c6<r2c5<r2c4<r2c3 ==> r2c7≠6
asc[2]: r1c7<r1c8<r1c9 ==> r1c9≠2, r1c9≠1, r1c8≠9, r1c8≠1, r1c7≠9, r1c7≠8
valley[5]: r3c4>r4c4>r5c4>r6c4<r7c4<r8c4 ==> r6c4≠6, r6c4≠5
hill[4]: r5c2<r6c2<r7c2>r8c2>r9c2 ==> r7c2≠4
str-asc[1]: r7c2<r7c1 ==> r7c1≠5
valley[4]: r3c2>r4c2>r5c2<r6c2<r7c2 ==> r5c2≠6
valley[5]: r3c4>r3c5>r3c6<r3c7<r3c8<r3c9 ==> r3c6≠5
- Code: Select all
Resolution state after Singles and whips[1]:
123456789 123456789 123456789 123456789 456789 3456789 1234567 2345678 3456789
3456789 123456789 56789 45678 34567 23456 12345 56789 6789
2345678 3456789 123456789 456789 23456 1234 23456 4567 5678
1234567 2345678 3456789 345678 456789 3456789 456789 3456 12345
123456789 12345 123456789 234567 345678 234567 1234 2345 3456789
123456789 234567 3456789 1234 234567 123456 2345678 3456789 123456789
6789 5678 234567 2345678 123456 3456789 234567 123456 123456789
123456789 34567 123456 3456789 2345678 1234567 345678 234567 123456
3456789 23456 12345 123456789 1234567 2345678 456789 123456789 123456789
521 candidates, 4695 csp-links and 7494 links. Density = 5.53%
x-wing-in-columns: n1{c5 c8}{r7 r9} ==> r9c9≠1, r9c4≠1, r9c3≠1, r7c9≠1
str-asc[1]: r9c3<r9c2 ==> r9c2≠2
str-asc[1]: r9c2<r9c1 ==> r9c1≠3
str-asc[1]: r9c2<r8c2 ==> r8c2≠3
whip[2]: r2n1{c7 c2} - r2n2{c2 .} ==> r2c7≠3, r2c7≠4, r2c7≠5
whip[2]: r4n1{c1 c9} - r4n2{c9 .} ==> r4c1≠3, r4c1≠4, r4c1≠5, r4c1≠6, r4c1≠7
whip[4]: r8c7{n8 n3} - r7c7{n7 n2} - r5c7{n2 n1} - r2c7{n1 .} ==> r9c7≠4
whip[4]: r2c5{n6 n7} - r2c4{n7 n8} - r2c9{n8 n9} - r2c3{n9 .} ==> r2c6≠6
g-whip[5]: c4n1{r6 r1} - c4n2{r1 r9} - r7c4{n2 n4+} - c4n3{r7 r4} - r5c4{n3 .} ==> r6c4≠4
whip[3]: r6c7{n8 n2} - r6c6{n6 n1} - r6c4{n1 .} ==> r6c8≠3
whip[7]: r3n1{c6 c3} - r3n2{c3 c1} - r3n3{c1 c2} - r4c2{n8 n2} - r5c2{n5 n1} - r2n1{c2 c7} - r2n2{c7 .} ==> r3c6≠4
whip[3]: r5c6{n7 n2} - r6c6{n6 n1} - r3c6{n1 .} ==> r4c6≠3
g-whip[7]: c7n9{r9 r4} - c7n8{r4 r6} - r8c7{n8 n6-} - c7n7{r8 r1} - r1c8{n6 n8} - r1c9{n7 n9} - c5n9{r1 .} ==> r9c7≠6
g-whip[7]: c7n9{r9 r4} - c7n8{r4 r6} - r8c7{n8 n5-} - c7n7{r8 r1} - r1c8{n6 n8} - r1c9{n7 n9} - c5n9{r1 .} ==> r9c7≠5
g-whip[11]: r7c7{n7 n2} - r2c7{n2 n1} - r5c7{n1 n4} - r5c8{n3 n5} - r4c8{n5 n6} - r3c8{n6 n7} - r3c9{n6 n8} - r2c9{n8 n9} - r2c8{n9 n8} - r1c8{n8 n5-} - r1c7{n7 .} ==> r8c7≠3
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Final resolution state:
123456789 123456789 123456789 123456789 456789 3456789 1234567 2345678 3456789
3456789 123456789 56789 45678 34567 2345 12 56789 6789
2345678 3456789 123456789 456789 23456 123 23456 4567 5678
12 2345678 3456789 345678 456789 456789 456789 3456 12345
123456789 12345 123456789 234567 345678 234567 1234 2345 3456789
123456789 234567 3456789 123 234567 123456 2345678 456789 123456789
6789 5678 234567 2345678 123456 3456789 234567 123456 23456789
123456789 4567 123456 3456789 2345678 1234567 45678 234567 123456
456789 3456 2345 23456789 1234567 2345678 789 123456789 23456789
Without the block constraints, it doesn't give much; the eliminations done by asc-chains are trivial; I've proven in [PBCS] that they are equivalent to whips[1] (I keep them here for illustration).
But this can give you an idea of the kind of rules used.
I tried to inject the final resolution state into SudoRules (the representations are compatible) in order to take advantage of the block constraints; it allows more eliminations, but it's not enough for a solution. In this puzzle, mixing the two kinds of constraints is necessary.
- denis_berthier
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Re: Can someone solve my first thermo-sudoku?
by denis_berthier » Wed Aug 11, 2021 6:54 am
gifmenger wrote:All horizontal and vertical thermometers with 3 or more squares are given.
On second thoughts, I realise I didn't use this.
A particular consequence should be that any given thermometer can't be extended and it is therefore ended on both sides by a length-one thermometer in the opposite direction. This is easy to represent as additional inequalities.
The given horizontal and vertical inequalities were:
- Code: Select all
------<<
-->>>>--
--->><<<
<<---->>
---->><<
-----<<-
>>--->>-
--->>->>
>>--<<--
->>-----
-->><<>>
----->>-
-->>><<-
>>->>>--
>>->>---
------<<
->>>----
->>-----
If I apply the above additional constraints, I get an extended set of inequalities:
- Code: Select all
-----><<
-<>>>><-
--<>><<<
<<>--<>>
---<>><<
----><<>
>><-<>><
--<>><>>
>><><<>-
<>><----
-<>><<>>
----<>><
-<>>><<>
>><>>><-
>><>><--
-----><<
<>>><---
<>><----
I'm aware this doesn't take into account all the non-allowed combinations of linear inequalities, but let's see if it's useful.
Now, FutoRules allows more eliminations and I can again inject the partial result into SudoRules and go farther than before into the resolution, but that's still not enough to solve the puzzle:
- for the same reasons as before (I don't use block and inequality constraints together);
- and for the additional reason that some non-allowed thermometer inequalities are not taken into account, because the negative constraint on thermometers of length three is not taken into account.
Regarding the first problem, I could iterate from FutoRules to SudoRules and vice-versa, with no guarantee that it would lead to a solution, because block and inequality constraints would still not be taken into together. I could also code a Sudoshiki variant in FutoRules.
Regarding the second problem, negative constraints are never easy to take into account. In the present case, I could easily add specific rules to take them into account.
However, I lack motivation to do any of this. Futoshiki with block constraints is already a not very popular variant of Futoshiki. Adding negative constraints will not make it more popularl.
- denis_berthier
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Re: Can someone solve my first thermo-sudoku?
by creint » Wed Aug 11, 2021 5:53 pm
- Code: Select all
.................................................................................
------<<-->>>>----->><<<<<---->>---->><<-----<<->>--->>---->>->>>>--<<--
->>------->><<>>----->>--->>><<->>->>>-->>->>---------<<->>>----->>-----
Results in
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145 48 1458 67 679 679 2 3 45
67 2 67 5 4 3 1 89 89
34 9 345 8 2 1 45 6 7
2 34 478 36 89 679 67 5 1
678 1 6789 2 78 5 3 4 89
35 357 89 1 367 4 67 89 2
9 78 2345 46 135 78 45 12 3456
14 6 134 9 35 2 8 7 345
78 35 23 3467 1356 678 9 12 46
Additional constraints:
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.................................................................................
-----><<-<>>>><---<>><<<<<>--<>>---<>><<----><<>>><-<>><--<>><>>>><><<>-
<>><-----<>><<>>----<>><-<>>><<>>><>>><->><>><-------><<<>>><---<>><----
Results in
- Code: Select all
1 8 45 7 6 9 2 3 45
67 2 67 5 4 3 1 9 8
3 9 45 8 2 1 45 6 7
2 4 8 3 9 6 7 5 1
67 1 67 2 8 5 3 4 9
5 3 9 1 7 4 6 8 2
9 7 23 46 13 8 45 12 456
4 6 1 9 5 2 8 7 3
8 5 23 46 13 7 9 12 46
It needs more constraints or it has multiple solutions.
- creint
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Re: Can someone solve my first thermo-sudoku?
by gifmenger » Tue Aug 17, 2021 3:27 pm
creint, thanks for your reply. It's very helpfull and clear. In your last result all single numbers were correct. So it should be solvable with extra information. Is there a way to come to an unique solution with a minimum of added information? Which number(s) should I add to the grid to make it solvable?
- gifmenger
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- Joined: 09 August 2021
Re: Can someone solve my first thermo-sudoku?
by creint » Tue Aug 17, 2021 7:01 pm
Here some example grids from the first solution.
Tried multiple times but all results in requiring 3 extra givens.
But with those starting givens it makes it easy.
You could also make r9c34 consecutive and r23c3 consecutive which will solve it without the need for givens. Can still be solved by advanced manual solvers. Only one layer of easy chains required.
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......................................6........................................24
...........7.............................................4.....................2.
.........6...................................................1..................4
.........6....................................................6.............1....
.........6................................................................36.....
Tried multiple times but all results in requiring 3 extra givens.
But with those starting givens it makes it easy.
You could also make r9c34 consecutive and r23c3 consecutive which will solve it without the need for givens. Can still be solved by advanced manual solvers. Only one layer of easy chains required.
- creint
- Posts: 393
- Joined: 20 January 2018
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