## A rather silly fish thermo

For fans of Killer Sudoku, Samurai Sudoku and other variants

### A rather silly fish thermo

I'm pretty sure that this sort of setup can never produce a unique puzzle without additional constraints (can probably prove it, even, though I haven't fleshed that out yet), but I came up with this silly proof of concept last week for a minimal (and aesthetically pleasing) constraint to make it work.

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`..98....7.6..5..4.3....21..7....35...1..6..8...49....25....19...8..4..3...27....6Thermo constraint: r5c3 is greater than r4c4`
Attachments
Swordfish Thermo.png (56.03 KiB) Viewed 386 times
mith

Posts: 803
Joined: 14 July 2020

### Re: A rather silly fish thermo

At the start, the PM is:
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`   124       245       9         8         13        46        236       256       7            128       6         178       13        5         79        238       4         389          3         457       578       46        79        2         1         569       589          7         29        68        124       128       3         5         169       149          29        1         35        245       6         457       347       8         349          68        35        4         9         178       578       367       167       2            5         347       367       236       238       1         9         27        48           169       8         167       256       4         569       27        3         15           149       349       2         7         389       589       48        15        6         `

And the thermo constraint amounts to setting r5c3=5 OR r4c4 ≠ 4

First trying to solve with r5c3=5 gives a trivial solution (with Singles):
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`459816327261357849378492165726183594915264783834975612543621978687549231192738456`

Trying to solve with r4c4≠4 also gives a trivial solution (with Singles):
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`459816327261357849378492165726183594915264783834975612543621978687549231192738456`

Miracle: the two solutions are the same.
denis_berthier
2010 Supporter

Posts: 3166
Joined: 19 June 2007
Location: Paris