Masyu ましゅ

Masyu (ましゅ) is a loop puzzle from the Japanese publisher Nikoli. Some cells of the grid hold a white or a black circle, called a pearl, and you draw one closed loop through the centers of cells, moving only horizontally and vertically. The loop never crosses or branches, it must pass through every pearl, and it may leave any number of plain cells unvisited. The pearls are the only clues: a white pearl means the loop goes straight through it and turns in a cell next to it, and a black pearl means the loop turns on it and then runs straight for two cells in both directions.

Masyu was designed to work without any numbers or letters, so the whole puzzle is built from those two kinds of circle. In English it is also known as Pearl, and it sits naturally beside Slitherlink and Yajilin, the other loop puzzles on this site.

On LogicPuzzles.io everyone gets the same daily 8×8 Masyu, and unlimited mode offers 6×6, 8×8 and 10×10 grids whenever you want another one. Every puzzle is checked by an exact solver to have exactly one solution, and by a deduction grader to be solvable without guessing. Undo, a timer and a Check button are built in, and your progress, streak and best times stay in this browser.

Start at the edges, where pearls have the fewest options. A black pearl needs two straight cells of room on both sides of its turn, so a black pearl on the border, or one row or column in from it, sends a leg two cells inward, and one in a corner is fixed completely. A white pearl on the border cannot go straight toward the wall, so the loop runs along the edge through it.

Next, look for pearl patterns. Two black pearls side by side can never be joined by a line, because the cells along a black pearl's legs must be straight and a black pearl is always a turn, so each one sends its leg away from the other. Three or more white pearls in a straight row cannot all be passed along that row, since the middle pearl would have no turn beside it, so the loop crosses every one of them at a right angle. Once you know which way a black pearl turns, draw both legs two full cells long.

Then use general loop logic. Every cell has either no line or exactly two, so a line end with only one open neighbor must continue that way, and a plain cell with only one usable neighbor can be marked ×. Never close a small loop early: a segment that would join the two ends of a path while pearls are still left outside cannot be part of the answer. And if the loop already runs straight through one neighbor of a white pearl, it must turn in the other.

The most common mistakes are forgetting the turn a white pearl needs and drawing a black pearl's leg only one cell long. Broken pearls and cells with more than two lines turn red as soon as they appear, a counter shows how many pearls are satisfied, and the Check button highlights any segment or × that does not match the solution.

Masyu was designed and published by Nikoli, the Japanese puzzle company that also created Slitherlink and Nurikabe. The idea was a puzzle that uses no numbers or letters at all: the only clues are white and black circles, which English speaking solvers call pearls, and the puzzle also appears under the name Pearl, for example in Simon Tatham's Portable Puzzle Collection. Nikoli's own Masyu puzzles have commonly been set on 10×10 grids and on larger 18×10 grids. In 2002 the mathematician Erich Friedman proved that solving pearl puzzles of arbitrary size is NP-complete, which puts Masyu alongside Slitherlink, Nurikabe and several other Nikoli puzzles that are known to be computationally hard.