### Solution/discussion of is.gd/kst_655_X

Posted:

**Monday 9. January 2023, 15:27**This was another fun&tricky one! Here's what I could come up with. The part in {squiggly brackets} isn't needed in hindsight, but it does make the solution easier IMHO. I'm curious what others find!

* C: naked quintuplet 56789 / hidden quartet 1234

* 5-fish 2 12789, which falls into place immediately thanks to X (H2=2)

* E5=3 (X)

* 3-fish 78 2/\ --> HP 78 @ B28 (alternatively: if 78 elsewhere in B --> skewed fish 2\, no 78 in /)

* Setti 7 / X: A8!=5 (otherwise A12=78, conflict B2)

* Inverse square rule: G7!=4

{

* no 3 in D, otherwise D8=5, G8=1 but D1=7 (Setti 7), A9!=9, G3=1=G8)

* Setti 3

* 2-fish 3 AC

* Gap B6

* UR: B5!=4 --> NT 569, gaps, A5=4

}

* Setti 5: F6!=4, otherwise 5 in all cols but not in A (X-wing 2 AC56)

* Skewed wing 5 /\

--> A9=9, most of the puzzle falls into place

* Setti 8 or 3-fish GHJ

* C: naked quintuplet 56789 / hidden quartet 1234

* 5-fish 2 12789, which falls into place immediately thanks to X (H2=2)

* E5=3 (X)

* 3-fish 78 2/\ --> HP 78 @ B28 (alternatively: if 78 elsewhere in B --> skewed fish 2\, no 78 in /)

* Setti 7 / X: A8!=5 (otherwise A12=78, conflict B2)

* Inverse square rule: G7!=4

{

* no 3 in D, otherwise D8=5, G8=1 but D1=7 (Setti 7), A9!=9, G3=1=G8)

* Setti 3

* 2-fish 3 AC

* Gap B6

* UR: B5!=4 --> NT 569, gaps, A5=4

}

* Setti 5: F6!=4, otherwise 5 in all cols but not in A (X-wing 2 AC56)

* Skewed wing 5 /\

--> A9=9, most of the puzzle falls into place

* Setti 8 or 3-fish GHJ