In a Total Masyu puzzle, one must draw a single loop through the centres of some cells according to the following rules:
- The loop may only travel horizontally or vertically, never diagonally; all turns are right-angled turns. The loop may only turn at the centers of grid cells. The loop may not cross itself or branch off; that is, from any cell centre, there can be only 0 or 2 loop segments extending from it. (Basically, it expects exactly as a loop in most loop logic puzzles behaves.)
- The loop must pass through every circle.
- The loop may not turn at a white circle, but must turn at at least one of the adjacent cells in the loop.
- The loop must turn at a black circle, but may not turn at either of the adjacent cells in the loop.
- A cell without a circle cannot behave as though it had one. Or rather, all possible circles that fit the solution are given.
Prove or disprove: The Total Masyu puzzle below has exactly one solution. (It doesn't contain any black circles; rule 4 above is present just for completeness.)
(This puzzle was originally published on my rather small blog here.)