- Arm
- One of the two straight segments leaving a black pearl. Each arm passes straight through the cell next to the pearl, so it is at least two cells long.
- Black pearl
- A filled circle. The loop must turn 90° on it and travel straight through the next cell in both directions. Sometimes called a black circle.
- Cell
- One square of the grid. The loop passes through cell centres, never along grid lines.
- Contradiction
- A situation that breaks a rule — such as a dead end, a branch, a black pearl passed straight through or a premature loop. Finding one proves the assumption that caused it is false.
- Cut
- An imaginary line dividing the grid into two parts, used in parity reasoning.
- Dead end
- A cell with only one possible exit. The loop can’t use it, so all its edges can be marked ✕.
- Edge
- The connection between the centres of two neighbouring cells. Each edge is either part of the loop (a line) or not (an ✕).
- Gray pearl
- A variant clue that may behave as either a white or a black pearl; the solver must decide which.
- Loop
- The single closed path you draw. It never branches, crosses itself or visits a cell twice.
- Loop end (loose end)
- The end of a partially drawn line segment. Every loop end must be extended until it connects to another.
- Masyu (ましゅ)
- The puzzle genre itself, originally published by Nikoli. Also called the pearl puzzle; formerly Shinju no Kubikazari and Shiroshinju Kuroshinju. See history.
- Parity
- The principle that a closed loop crosses any closed boundary an even number of times, following from the Jordan curve theorem.
- Pearl
- A circle clue — white or black. The name Masyu itself comes from a misreading of the Japanese word for pearl.
- Premature loop (short circuit)
- A closed loop that leaves out some pearls or line segments. Joining two adjacent ends of the same segment is forbidden unless it completes the whole puzzle.
- Propagation
- The chain reaction of deductions that follows a new line or ✕: neighbouring pearls, loop ends and dead ends often resolve one after another.
- Unique solution
- A puzzle with exactly one valid loop. All MasyuPuzzles.com puzzles are verified to be unique.
- What-if chain
- A short trial: assume an edge is a line or ✕, follow the direct consequences, and reject the assumption if it leads to a contradiction. Needed on Hard puzzles.
- White pearl
- An open circle. The loop goes straight through it and turns in the cell before or after it, or both.
- ✕ mark
- A note that an edge is not part of the loop. Marking ✕ is as important as drawing lines.
Learn how these ideas work in practice in our Masyu strategy guide.