Rules: Draw a single closed loop passing through adjacent squares,moving only horizontally or vertically.The loop cannot visit any square more than once.At every white circle,the loop must go straight and turn on either or both of the squares visited immediately before and immediately after.At every black circle, the loop must turn,and go straight through both the squares visited right before and right after.Additionally,after the puzzle is solved,you cannot legally place a circle of the same color orthogonally adjacent to any of the given circles.
At first, I thought this puzzle had multiple solutions in the lower-left quadrant. Then I saw it had no solutions--at least, not if I understood the additional rule correctly.
ReplyDeleteThe path through the black circle at R1C7 must turn and go two squares to the side. So it must be possible to place a white circle in R1C8 (or R1C6 if things are really crazy), but this is right next to the white circle at R1C9 (or R1C5), which I think the rule specifically disallows.
I had the same 2 observations.
DeleteYour observation is correct.The circle at R1C9 has to be at R1C8, and a white circle has to be there at R8C2.
ReplyDeleteIt still doesn't seem to be unique in the left bottom corner.
DeleteThere are still three solutions: two that visit R10C1 and one that doesn't. That last one was probably your intended answer, but there's no way to add a clue to specify it. However, if you add an otherwise-illegal black circle to R7C5, there's a unique solution.
DeleteMy intended solution was the other one of the two that visit R10C1. Yes, that did fix it.
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