# Mixed-breeds are puzzles too!

This is a three-dimensional mixed-breed puzzle. The five squares depict the five layers of a $$5\times5\times5$$ cube. The goal is to solve the odd-numbered layers as yajilin and even-numbered layers as masyu.

Short rules:

• Shade some cells on odd-numbered layers. The numbered cells show how many shaded cells are in the direction of the arrow.
• Shaded cells cannot be adjacent to another shaded cell, but they can touch the numbered cells.
• Unshaded cells on each yajilin layer are all connected in 2D (i.e. each layer is treated separately).
• Make a single loop in 3D space which goes through every unshaded cell on odd-numbered layers, and every circle on even-numbered layers.
• A line passing through a white circle must continue straight through its cell and make a turn in the directly following or preceding cell (or both).
• A line passing through a black circle must make a turn inside that cell and continue straight for at least one cell on both sides.

Note: Feel free to use any notation you feel the most comfortable with, as long as it's properly explained. My way is to use diagonal lines to show movement between layers.

• Just a 3d Yajalin left to do :) (I was thinking about the arrows, you could use NESWUD) – JMP Aug 7 '19 at 10:23
• @JonMarkPerry Maybe I'll try that next! – Jafe Aug 7 '19 at 10:31
• Or even a 4d Masyu!!! – JMP Aug 7 '19 at 10:46

## 1 Answer

Observations

The Masyu layers behave like they do in the previous 3D variants.
The usual Yajilin rules of dead ends only apply when the layer above and below is blocked as well. The 2D-connectivity allows easy deductions.

Finished grid