The one-solution trick
Filoop promises that every level has exactly one solution. On hard levels you can turn that promise into a solving tool.
One solution, checked
Filoop’s generator checks each level with a solver and keeps it only if there is exactly one way to solve it. You never need this fact to solve a level — forced moves and dead-end checks are enough. But when they run out, it can save a lot of trial and error.
Two fillings mean a wrong turn
Imagine your plan leaves a closed room for a single thread, with its two buttons in opposite corners of a 3×3 square. The thread can snake row by row or column by column — both versions cover the room. A Filoop level can’t have two solutions, so the real solution never creates this room. Something earlier in your plan is wrong.
Why this holds: if the finished solution contained such a room, you could refill the room the other way and get a second, equally valid solution. The generator would have rejected that level.
How to use it
When you are choosing between two options, play each a few steps ahead. If one of them leaves an area that could be filled in two different ways, drop it and take the other.
It is most useful near the end of a level, when few empty cells are left and every option fits in your head. Look at the remaining cells and ask whether they can be filled only one way. If you see two, step back a couple of moves.
Signs of such an area:
- a closed room with a single colour inside and room to spare;
- two threads that could swap a pair of cells between them without breaking anything;
- a stretch where a thread could make a detour or skip it, and both versions fill the board.
Be careful with it
The trick only tells you that a plan is wrong, not which part of it. It also depends on seeing the alternative correctly: if you missed a cell, the “second solution” may not exist at all. Use it to choose between two candidate moves, not to throw away a whole plan.
One more trap: two drawing orders are not two solutions. If the threads end up in the same cells whichever way you draw them, that is one filling.
Order of tools: border first, then forced moves, then dead-end checks, and only then the one-solution trick.
Levels where it pays off: the hardest set, with 8×8 and 9×9 boards. Or test yourself on today’s daily puzzle.