Masyu

A pure-logic loop puzzle from Japan, published by Nikoli and known worldwide by its Japanese name. White and black pearls are scattered over the board, and your job is to thread one single closed loop through every one of them. The loop must run straight through a white pearl and turn on a black one, and each 6×6 board here has exactly one solution.

How to play

The loop travels from cell centre to cell centre, horizontally and vertically. When you are done it has to be one single closed ring — never crossing itself, never branching into a third direction, never leaving a loose end. Cells without a pearl may be left empty, but every pearl must lie on the loop.

A white pearl is a "go straight" pearl: the loop enters and leaves it in the same direction. It may not sit in the middle of a long straight run, though — the loop has to turn in at least one of the two cells directly next to it.

A black pearl is a "turn" pearl: the loop makes a right-angle turn on it. On top of that, the loop must carry on straight for at least one more cell in both of the directions it leaves the pearl in.

Drag your finger across the board to lay down segments as you go, and drag back along a line you have already drawn to rub it out. A single tap on the gap between two neighbouring cells toggles just that one segment. Pearls turn green while they satisfy their rule and red when they break it, so mistakes surface early. Each board has exactly one solution, and your finishing time is your score.

Tips & strategy

Start at the walls, because the border does half of your thinking for you. A white pearl on the top or bottom row cannot run vertically — there is no room to go straight through — so it must run along that row, and the same logic pins white pearls on the left and right columns to their column. A black pearl on an outer row cannot leave towards the wall, so one of its two directions is already fixed. A black pearl in a corner is impossible outright.

The gap between two black pearls sitting side by side is never used. If the loop travelled from one to the other, it would have to carry on straight through the second pearl for a cell — but a black pearl must turn. Ruling that segment out immediately shapes the region around both of them.

Three white pearls in a straight line can never all be crossed along that line. The middle one would then have straight-running neighbours on both sides and no turn next to it, which its rule forbids. So somewhere in that run the loop has to cut across perpendicular instead, and pinning down where usually unlocks the rest of the board.

Think in exits rather than in lines. Every cell the loop touches has exactly two, and the moment a cell has its two segments, every other side of it is closed for good. That is why black pearls are the best opening move: each one hands you three cells of certainty in a single stroke — the turn itself plus a forced segment on either side — while a white pearl only fixes the direction it is crossed in.