Masyu Puzzles
One closed loop, straight through every white circle and turning on every black one. Tap between two cells to draw a line, again to cross it off. Every grid is solvable by pure deduction — no guessing anywhere.
Also written mashu, and sometimes called the pearl puzzle after its white and black beads.
Related Practice
What Is A Masyu Puzzle?
Masyu gives you a grid with white and black circles scattered across it, and asks for a single closed loop running between the centres of neighbouring cells. The loop never crosses itself and never branches. What the circles do is tell you how the loop behaves as it passes through them: it goes straight through a white one and turns on a black one — and each kind carries a second condition about the cells immediately either side. It was named by Nikoli, the Japanese publisher, and the name means "pearl".
The Two Circles, And What Each Really Says
Most of masyu is learning how much each circle tells you. They are not equally strong:
| Circle | At the circle | Either side | Cells fixed |
|---|---|---|---|
| White | The loop passes straight through | At least one of the two neighbours must turn | 1 firmly, 2 loosely |
| Black | The loop turns | Both neighbours are passed straight through | 3 firmly |
That difference is why the grids here come in two characters. A board clued mostly by white circles asks you to build the loop up from small certainties; one with several black circles hands you three-cell chunks straight away and then gets tight. Neither is harder in general — they are different puzzles.
The loop does not visit every cell. In these puzzles roughly one cell in ten is left off it. That is deliberate: a masyu whose loop always covered the whole grid would carry a rule nobody told you, and a solver who spotted it would get an advantage the puzzle never meant to give. Do not assume an empty-looking cell must be used.
Where A Masyu Opens
Always at the edges, and always at black circles first. A black circle has to turn and then run straight for two more cells in both directions, which is a lot to fit — so one on the top row cannot go upward at all, and is immediately forced downward and down again. A black circle in a corner is nearly self-solving. White circles on an edge are the other free move: a white on the top row cannot be crossed vertically, so it must be crossed sideways.
The Rule That Settles More Than Any Other
Once a few lines exist, the most productive question is not "where does a line go" but "where can a line not go". If drawing a particular line would close a small circuit while circles still sit outside it, that line is impossible — the answer is one loop through every circle, not several. Crossing those off is what makes the next line findable, and it is the single deduction that does the most work here. The hint button names it when it applies.
Why The Boards Stop At 8×8
Every grid on this page is proved before you see it: a solver restricted to ordinary deduction must finish it with every gap decided, which also makes the answer unique, since each step was forced. Boards larger than 8×8 do get generated, but the share that can be finished without guessing falls away sharply, and a page that has to try thousands of candidates is a page that keeps you waiting. At 6×6 to 8×8 every grid here is built and proved in well under a second.
Masyu Puzzles Frequently Asked Questions
What is a masyu puzzle?
A Japanese loop puzzle. Draw one closed loop through the centres of neighbouring cells, never crossing or branching. White circles are crossed straight; black circles are turned on.
What are the rules of masyu?
Three. One closed loop through cell centres, moving only up, down, left or right. At a white circle it goes straight through and turns in at least one cell either side. At a black circle it turns, and runs straight through both cells either side.
Does the loop have to visit every cell?
No. Cells without a circle may be left off the loop, and here roughly one cell in ten is unused. That is deliberate: a loop that always covered everything would be an unstated extra rule.
Where do you start a masyu?
At the black circles nearest an edge. A black one on the top row cannot go up, so it must go down — and then straight on for a second cell. A corner black is nearly self-solving. White circles on an edge are the other free start.
Why are black circles the stronger clue?
A black circle constrains three cells at once — itself and the two it runs straight through. A white one pins one cell hard and its neighbours only loosely, which is why an all-white grid usually is not unique.
What does crossing an edge off actually do?
It records that no line runs between those two cells — and it is half the technique. A cell only forces a line once its other sides are gone. Solvers who only draw and never cross tend to stall.
Can two black circles sit side by side?
They can be adjacent on the grid, but the loop can never join them directly — that would mean leaving a black circle straight. So the edge between two adjacent blacks is always crossed off.
Does every puzzle here have one answer?
Yes, and none needs guessing. A solver restricted to ordinary deduction must finish it with every edge decided; because each step is forced, the answer is the only one. An exhaustive count re-checks that independently on the smaller boards.
What does masyu mean?
It means "evil influence", and the name is an accident. Nikoli originally published it as Shinju no Kubikazari — "pearl necklace" — which is what the white and black circles are meant to be. The story goes that the president of Nikoli misread the kanji for "pearl", the misreading was funnier than the original, and Masyu stuck.