## Advanced techniques required to solve 4x4 Sukakus

For fans of Killer Sudoku, Samurai Sudoku and other variants

### Advanced techniques required to solve 4x4 Sukakus

A Sukaku is a pencilmark only Su-Doku. There has been a thread on ordinary-sized Sukakus in this forum. But not 4x4 ones.

So I looked into those and I have discovered that some advanced techniques are required to solve some 4x4 Sukakus.

Here is one which I created:
Code: Select all
`2313 4132 1132 24314234 3132 4132 13423311 4213 1432 21214234 4312 2413 2224requires turbot fish`

and another one:
Code: Select all
`1123 4312 3132 13424231 2212 4321 13243111 1423 1423 21124423 2341 2431 2442requires finned x-wing`

Both puzzles also have a Sue de Coq which eliminates four candidates but does not crack the puzzle. The second puzzle has an XYZ-wing which eliminates one candidate but also does not crack the puzzle.
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Once upon a time I was a teenager who was active on here 2007-2011
999_Springs

Posts: 367
Joined: 27 January 2007
Location: In the toilet, flushing down springs, one by one.

### Re: Advanced techniques required to solve 4x4 Sukakus

999_Springs wrote:... and another one:
Code: Select all
`1123 4312 3132 13424231 2212 4321 13243111 1423 1423 21124423 2341 2431 2442requires finned x-wing`

This puzzle doesn't have a valid solution.

Turbot fish on 4: r1c24+r3c23 => r2c3, r4c4<>4
=> r34c4=[12] => r34c1=[34] => r34c2={12}
=> No candidate for r2c2 (invalid)

On the other hand changing r4c1 to "1423" will make it a valid puzzle...

But then it doesn't really "require" a finned x-wing (the turbot fish on 4 is enough to solve it)...

No matter what I think it doesn't take anything further than a turbot fish to solve all these...
udosuk

Posts: 2698
Joined: 17 July 2005

999_Springs wrote:
Code: Select all
`1123 4312 3132 1342 4231 2212 4321 1324 3111 1423 1423 2112 4423 2341 2431 2442 requires finned x-wing  `

Actually r4c3=2142.

edit: actually r3c4=2142 and r4c3 remains unchanged.
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Once upon a time I was a teenager who was active on here 2007-2011
999_Springs

Posts: 367
Joined: 27 January 2007
Location: In the toilet, flushing down springs, one by one.

Oops.

I didn't see that the turbot fish involving strong links r1c24 and r24c1 on 4 would eliminate 4 from r4c4 which also solves the puzzle in the same way as the finned X-wing. I'm not very good at spotting turbots when the strong links aren't parallel to each other.

Oh well. If finned x-wing is before turbot fish in your hierarchy of solving techniques then it does need one.

However, I have discovered that you can have Sukakus made from 3x3 Latin squares which need XY-wings.

Here is one I created:

Code: Select all
`122 232 321311 213 112312 221 132`

I think that this is the smallest that you can get.
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Once upon a time I was a teenager who was active on here 2007-2011
999_Springs

Posts: 367
Joined: 27 January 2007
Location: In the toilet, flushing down springs, one by one.

999_Springs wrote:However, I have discovered that you can have Sukakus made from 3x3 Latin squares which need XY-wings.

Here is one I created:
Code: Select all
`122 232 321311 213 112312 221 132`

Is the solution unique for this one? I found 2 solutions:
Code: Select all
`1 3 23 2 12 1 32 3 13 1 21 2 3`
udosuk

Posts: 2698
Joined: 17 July 2005

AAAAAARRRRRRGGGGGGHHHHHH!!! r1c3=331.

Sorry.

(curses keyboard)
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Once upon a time I was a teenager who was active on here 2007-2011
999_Springs

Posts: 367
Joined: 27 January 2007
Location: In the toilet, flushing down springs, one by one.

Has anyone managed to solve my 3x3 Latin square Sukaku without using an XY-wing or a forcing chain yet?
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Once upon a time I was a teenager who was active on here 2007-2011
999_Springs

Posts: 367
Joined: 27 January 2007
Location: In the toilet, flushing down springs, one by one.

999_Springs wrote:Has anyone managed to solve my 3x3 Latin square Sukaku without using an XY-wing or a forcing chain yet?

It's just a tiny puzzle, nothing to get excited about...

This is the standard pencilmark form:
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`#12   23  #13#13   123 #12 123  12   123`

The # cells form 2 UR-type-3s (I think) simultaneously, so both r2c13 cannot be 1.
Therefore r2c2=1, solving the puzzle.

Alternatively, if uniqueness assumption is not desirable,
Code: Select all
`-12  *23  @13@13  *123 -12 123  12   123`

We have a y-wing on offer here (refer to this link)...

The {13} pointing pair (@) together with the strong link of 3s on c2 (*) eliminate the 1s from r1c1+r2c3.

I don't think this move is much easier than the xy-wing, but it's definitely more elegant than any forcing chain...
udosuk

Posts: 2698
Joined: 17 July 2005