Summary: Masyu rules explained — draw one closed loop that runs straight through every white pearl and turns on every black one. Includes the openings that crack a board fast and a worked 6 × 6 example.
What Is Masyu?
Masyu is a Japanese loop-logic puzzle, sold here as Pearl Logic. The board is a plain grid with two kinds of pearl on it — open white circles and filled black ones — and it asks one question: where does the loop go?
Your job is to draw one closed loop through the centres of cells so that every pearl on the board is satisfied. There are no numbers to add, no words to know and nothing to translate — just two kinds of circle and one line that has to obey them both.
The pearls do not tell you how many lines to draw or where to begin. Each one places a single local constraint on the loop, and those constraints interlock until exactly one circuit survives. Finding it is pure deduction, never a guess.
Masyu Rules
- The loop runs horizontally and vertically only. Never diagonally.
- The loop never crosses itself and never branches. Every cell is either untouched or has exactly two loop segments meeting in it. No dead ends, no T-junctions, no crossings.
- There is exactly one loop — a single closed ring, not two or more separate ones.
- The loop passes through every pearl. No pearl may be left stranded off the circuit.
- A white (open) pearl: the loop goes straight through it — and turns in at least one of the two cells the line enters and leaves through.
- A black (filled) pearl: the loop turns on it — and goes straight through both of the cells the line enters and leaves through.
- The loop does not have to visit every cell. Cells with no pearl may be left empty.
Two of those need a picture before they will stick.
The Two Pearl Rules, Side by Side
A white pearl fixes three cells: itself, and the cell on each side of it. A black pearl fixes five: itself, plus two cells in each of its two directions — because each arm has to keep going straight through the cell it lands in. That reach is what makes the pearls so powerful.
White pearl — straight here, turn nearby. The loop must pass straight through the pearl, either left-to-right or top-to-bottom. It must then turn in the cell it came from, the cell it goes to, or both. A white pearl the loop sails straight through and straight past on both sides is illegal.
Black pearl — turn here, straight either side. The loop must make a right-angle turn on the pearl, so one arm leaves horizontally and the other vertically. Each of those arms must then continue straight through the very next cell before it is allowed to do anything else.
Read them as a pair and the shape of the puzzle appears: white pearls are corridors that must bend somewhere close by, and black pearls are corners that need a clear run-up on both sides.
Empty Cells Are Part of the Answer
The rule that surprises people arriving from Sudoku or Nonograms is that the loop may skip cells entirely. Here is a 7 × 7 board where it does — the three cells in column 3, rows 1 to 3 are never touched:
You will see this most on the odd-sided square boards — 5 × 5, 7 × 7 and 9 × 9 — because a grid with two odd sides cannot be covered by a loop completely. On a board with an even side, the loop usually does end up reaching every cell, so do not treat a full grid as a sign you have gone wrong.
How to Solve a Masyu Puzzle
The fastest openings come from pearls that have run out of room. Start at the edges.
- Black pearls in a corner are free moves. A black pearl needs two clear cells in each of its two directions — it turns on the pearl, then runs straight through the next cell. In a corner, only two directions have any room at all, so both arms are forced immediately, and each arm gives you two more cells of line: out of the pearl, through the next cell, and into the one after it.
- Black pearls near an edge give you one arm. The same rule applies one cell in. A black pearl in the top two rows cannot send an arm upward — there isn’t room to turn and then continue straight — so its vertical arm must point down. Same logic for each of the other three edges.
- White pearls on an edge run along it. A white pearl needs the loop to pass straight through, which takes a cell on both sides. A white pearl in the top or bottom row therefore runs horizontally; one in the left or right column runs vertically. (This is also why you will never see a white pearl in a corner — no direction has room, so no valid board contains one.)
- Two black pearls side by side push apart. The loop cannot run along the segment joining them: each would need the other to go straight, but a black pearl turns. So the edge between two orthogonally adjacent black pearls is always empty, and each pearl’s arm on that side must point the other way.
- Watch for the straight-through-three trap. When the loop runs through a white pearl, it cannot also run straight through both the cell before and the cell after. If you have already forced one neighbour straight, the other one must turn.
- Never close a small loop early. A ring that closes while a pearl is still outside it is dead on arrival — there is only ever one loop, and it must collect every pearl. Whenever a line is about to join back onto itself, check whether every pearl is already aboard.
- Rule cells out as you go. A cell with no line yet and only one direction still open can never be on the loop, because it would need two. Mark a link you have ruled out with a small × between the two cell centres, and put a dot in a cell that can never be on the loop at all. Ruling cells out is as useful as drawing segments, and on a dense board those crosses do more work than the lines.
A Worked Start
Here is a real 6 × 6 Easy board with its answer, both gridded so you can follow along by row and column. Rows are numbered top to bottom, columns left to right.
Work the corners first.
- Row 1, column 1 is a black pearl in the top-left corner. It cannot point up or left. So its two arms go right and down, and each must run straight through the next cell: the loop goes r1c1 → r1c2 → r1c3, and r1c1 → r2c1 → r3c1.
- Row 1, column 6 is a black pearl in the top-right corner. By the same argument its arms go left and down: r1c6 → r1c5 → r1c4, and r1c6 → r2c6 → r3c6.
- Row 6, column 1 is a black pearl in the bottom-left corner — arms right and up: r6c1 → r6c2 → r6c3, and r6c1 → r5c1 → r4c1.
Three corners have now drawn a large part of the border for you. Next, the most satisfying deduction on this board:
- Row 2, column 5 is a black pearl with no room in two directions. It sits one row from the top, so it cannot point up. It also sits one column from the right edge, so it cannot point right — there is no cell beyond r2c6 for the arm to continue straight into. Both arms are forced: left and down. That gives you r2c5 → r2c4 → r2c3 and r2c5 → r3c5 → r4c5 in a single step.
Now push past the free moves, using the same rule twice more.
- Row 2, column 2 is a black pearl boxed in on two sides. One row from the top means no upward arm; one column from the left means no leftward arm. Forced right and down: r2c2 → r2c3 → r2c4, and r2c2 → r3c2 → r4c2. Notice that r2c3 was already committed by the r2c5 deduction — the two agree, which is exactly the confirmation you want.
- Row 6, column 4 is a black pearl in the bottom row. It cannot point down, so its vertical arm is forced up: r6c4 → r5c4 → r4c4. Its horizontal arm has room on both sides, so hold off on that one until a neighbour decides it.
Cross-check the white pearls you have committed to. Row 1, column 2 is white in the top row, so it had to run horizontally — which is what the corner pearl at r1c1 forced. Row 2, column 1 is white in the left column, so it had to run vertically — again, already drawn. Agreement like this is a good sign; a contradiction would mean backing up.
The rest follows from rule 7 — try it before you look. From here the board closes itself: each new segment starves its neighbours of options until the single loop in the picture is the only thing left.
Why Every Puzzle Is Fair
Puzzle Maker Pro generates a Masyu board by drawing a random closed loop first, working out the complete set of pearls that loop implies, and then removing pearls one at a time — keeping a removal only when the board still solves by pure deduction from an empty grid.
Two guarantees fall out of that, at every difficulty band:
- Exactly one solution. Never two valid loops.
- No guessing, ever. Difficulty is set mainly by how many pearls survive the thinning: Easy leaves you nearly every pearl the loop supports, and Expert strips out about half of them. Same rules, less scaffolding — a sparse Expert board never asks you to try something and see.
FAQ
What are the rules of Masyu?
Draw a single closed loop through cell centres, moving only horizontally and vertically. It may never cross or branch, it must pass through every pearl, it runs straight through each white pearl and turns in at least one neighbouring cell, and it turns on each black pearl and runs straight through both neighbouring cells. Cells without pearls may be left empty.
Does a Masyu loop have to go through every cell?
No. Only the pearls must be on the loop. Cells with no pearl can be left empty — most visibly on the odd-sided square boards, where the loop cannot cover the grid completely.
Can a Masyu puzzle have more than one solution?
No. Every Masyu puzzle generated in Puzzle Maker Pro has exactly one solution — a board is only accepted if a non-branching solver drives it to a single complete loop from an empty grid, which also proves no guessing is needed.
Can the Masyu loop touch or cross itself?
It can never cross, and it never branches — every cell on the loop has exactly two segments. Two separate stretches of the loop can, however, run alongside each other in neighbouring cells, which is common on dense boards.
What is the difference between a white pearl and a black pearl?
White means the loop goes straight through and must turn in at least one neighbouring cell. Black means the loop turns on the pearl and must go straight through both neighbouring cells. White is a corridor; black is a corner.
What Masyu board sizes are there?
Seven squares — 5 × 5, 6 × 6, 7 × 7, 8 × 8, 9 × 9, 10 × 10 and 12 × 12 — plus six rectangles: 8 × 6, 6 × 8, 10 × 8, 8 × 10, 12 × 10 and 10 × 12. There is no 11 × 11: on boards with two odd sides the generator’s success rate falls away above 9 a side, so those are left out.