Masyu (Pearls) Puzzle

Masyu is a loop puzzle, and it is also called Pearls. You draw one closed loop through the centres of the cells, and black and white pearls tell you where it must turn and where it must run straight. You can play a 6×6 or an 8×8 grid, and every puzzle here has exactly one solution that you can reach by logic, with no guessing.

Rules

The board is a grid of cells, and some cells hold a white or a black pearl. A line joins the centres of two cells that sit next to each other across or down, never diagonally.

Draw lines to make a single closed loop. The loop never crosses or touches itself and never branches, so every cell on it has exactly two lines and every other cell has none. The loop doesn’t have to visit every cell, but it must pass through every pearl.

On a black pearl, the loop turns a corner. Both arms then go straight through the next cell, so the loop can’t turn again in the cell right after the pearl on either side.

On a white pearl, the loop goes straight through. It must turn in at least one of the two cells on either side of the pearl along the loop. It may turn in both.

The puzzle is solved when the lines form one loop that passes through every pearl the right way. Segments you leave empty don’t need a cross.

Controls

Tap between two neighbouring cells to draw a line joining their centres, and tap the line again to clear it. A tap right on a cell centre does nothing, so aim for the gap between two cells. To draw several segments at once, press on a cell and drag from cell to cell; dragging back over the last step takes it off again before you let go.

Switch the tool under the board to Cross to mark segments that can’t be part of the loop. With a mouse, a right-click or a right-drag always draws crosses. Starting a drag on a segment that already has the tool’s mark clears instead, so the same gesture erases a run.

A cell with three or more lines, a white pearl where the loop bends or runs straight on through both neighbours, a black pearl the loop runs straight through or whose arm can no longer go straight, and a small closed loop while other lines are still elsewhere all turn red at once. A finished loop that misses a pearl turns that pearl red. Press Hint for one segment the rules already force, with a sentence saying why. Press Check when you want the board checked against the rules. Undo and Redo step through your moves, and Reset clears the board. When the loop is right, it turns teal.

On a keyboard, the arrow keys move a cell cursor, Shift with an arrow toggles the segment leaving that cell, and X switches between Line and Cross.

Techniques

Easy grids follow from the pearls alone:

• White pearls on the border: a white pearl on the edge of the grid can’t go straight across it, so the loop runs along the border through that pearl.
• Blocked white pearls: a white pearl runs either across or down. If a cross or the border rules one way out, the loop takes the other, and one line touching the pearl fixes its direction.
• Black pearls near a wall: each arm of a black pearl needs two straight cells. If one direction runs into the border or a cross within two cells, the arm goes the opposite way.
• Black pearls side by side: the loop never runs directly between two neighbouring black pearls, so each one sends its arm away from the other.
• Three white pearls in a row: the loop can’t run along all three, so it passes through each of them at right angles to that row.
• White pearls must turn: if the loop already runs straight on past a white pearl on one side, it has to turn on the other side.

Medium grids also need following the line through empty cells. A cell with two lines is full, so its other sides are empty. A cell with one line and one open side must continue through it, and a cell with no line and only one open side is a dead end, so that side stays empty.

Hard grids need a wider view:

• No early loops: a segment that would close a loop while some pearl is still off it can’t be a line.
• Parity: the loop is closed, so it crosses any straight cut between two rows or two columns an even number of times. If only one segment across the cut is still open, the count decides it.

Beginner tips

Start with the pearls on or next to the border. A white pearl on the border runs along it, and a black pearl one cell from the border sends that arm the other way.

Draw both arms of a black pearl as soon as you know them, two segments each. Those fixed corners usually settle the white pearls near them.

Use crosses freely. A crossed segment makes the next step around a pearl easier to see. If you are new to Masyu, start with the daily 6×6 easy grid, and move up to 8×8 once the black pearl corners feel natural.