Edit 5/16/2018 - See my other answer. I’ve made available a fully functional demo of this in the first person template game type. Check my other answer below!
**You can download the project files, add to your Unreal Projects Folder, and take a look at all the Blueprints/Actors in the Slider_Puzzle folder: **
Many thanks to these two for providing the much needed legwork in how to accomplish this.
- Phaser - HTML5 demonstration I lifted the logic from
- https://www.cs.bham.ac.uk/~mdr/teaching/modules04/java2/TilesSolvability.html - brilliant breakdown on checking validity of the puzzles.