What Is Masyu?

Masyu (pronounced mah-shoe) is a logic puzzle published by the Japanese puzzle publisher Nikoli — the same company that popularized Sudoku worldwide. The name roughly translates to "evil influence," a nod to how pearls on the grid seem to exert invisible forces on the loop you draw.

Unlike Sudoku (number placement) or crossword puzzles (vocabulary), Masyu is purely spatial. There are no numbers, no letters, and no hidden information. Every puzzle is solvable from the starting pearls using only logical deduction.

If you enjoy Number Link connect puzzles, Masyu shares the loop-drawing DNA but adds far richer constraints through pearl interactions.

The Rules of Masyu

The rules look simple — two pearls, two constraints — but the emergent logic is deep.

The Universal Rules

Every Masyu puzzle shares these non-negotiable rules:

Black Pearl Rule (●)

When the loop reaches a black pearl, it must:

1. Turn at the black pearl (make a 90° corner)
2. Continue straight for at least one full cell immediately before the black pearl
3. Continue straight for at least one full cell immediately after the black pearl

In plain language: the loop cannot pass straight through a black pearl — it must corner there. And on both sides of that corner, the loop gets at least one straight cell before it can turn again.

White Pearl Rule (○)

When the loop reaches a white pearl, it must:

1. Pass straight through the white pearl (no turn at the pearl itself)
2. Turn in at least one of the two adjacent cells (before OR after the white pearl) — or both

The white pearl forces straight passage, but the loop must prove its visit was "genuine" by making a turn immediately next to it — on the entry side, the exit side, or both.

Pearl Constraint Comparison

This comparison is the key insight: black and white pearls are opposite constraints. Black demands a turn at the pearl; white forbids it. Black extends straight away from the pearl; white's straightness is only at the pearl.

Your First Masyu: Step-by-Step Walkthrough

Let's solve a small scenario together. No prior experience needed.

The Setup

Imagine a 5×5 grid. Place three black pearls:

• Black at (row 2, col 2)
• Black at (row 3, col 4)
• Black at (row 4, col 2)

And two white pearls:

• White at (row 1, col 4)
• White at (row 3, col 2)

Initial puzzle state: 3 black pearls (●) and 2 white pearls (○) on a 5×5 grid

Step 1: Start at the Border

White pearls on the outer border are the easiest starting clues. Our white pearl at (1,4) sits on the top edge. A loop passing straight through it along the top edge must travel horizontally (parallel to the border) — because vertical straight passage would immediately hit the grid boundary.

Step 2: Black Pearls Near the Border

Our black pearl at (2,2) is one cell from the left edge and one from the top. The rule says straight segments must extend at least one cell on both sides of the turn. If the turn at (2,2) went toward the top-left corner, neither straight segment could extend far enough without hitting the edge illegally.

Step 3: Chain the Constraints

The white pearl at (3,2) requires straight passage. Since the adjacent black pearl at (2,2) already forces a specific geometry, the white pearl's straight-through rule cascades — it forces the loop at (3,2) to continue in whatever direction the local geometry allows.

Step 4: Avoid Short Circuits

As you draw, you'll sometimes be tempted to close a small loop connecting two nearby segments. Resist. The loop must visit EVERY pearl before closing. A short circuit that skips pearls is an invalid solution.

Step 5: Finish the Loop

Once all pearls are threaded and no short circuits are formed, connect the remaining open endpoints. A correctly-solved Masyu has exactly one continuous curve — no loose ends.

Black Pearl Patterns (with Grid Visuals)

Black pearls are your strongest starting clues. Here are the mandatory patterns.

Pattern A: Black Pearl on the Edge

┌───┬───┬───┐
│   │ ● │   │   ← Black on top edge
└───┴───┴───┘

A black pearl on the top edge (row 1) cannot extend straight upward — there's no cell above. Therefore both straight segments must extend downward, and the turn must face the interior.

Pattern B: Two Adjacent Black Pearls

┌───┬───┐
│ ● │ ● │   ← Two blacks side by side
└───┴───┘

Each black pearl needs straight extensions of at least one cell. If both tried to extend toward each other, they'd collide (the loop can't cross itself). Therefore both must extend away from each other.

Pattern C: Black Pearl in a Corner

┌───┬───┐
│ ● │   │   ← Black in top-left corner
├───┼───┤
│   │   │
└───┴───┘

A corner black pearl has two borders constraining it. The loop must turn at the corner AND extend straight on both sides — meaning the loop path through a corner black is completely forced: one cell down and one cell right (for a top-left corner), forming a fixed L-shape.

White Pearl Patterns

White pearls are subtler but equally powerful once you learn to read them.

Pattern A: White Pearl on the Border

A white pearl on the top edge must be traveled straight through horizontally (parallel to the border). Vertical passage would run into the grid edge immediately.

Pattern B: Two Adjacent White Pearls on the Border

Two white pearls next to each other along the border both require straight passage. Beyond the pair, the loop must turn (at least one turn in adjacent cells for each pearl).

Pattern C: Three-in-a-Row White Pearls

Three white pearls in a straight line cannot all be passed straight through in the same direction — the middle pearl would have no turn adjacent to it (violating the white pearl rule). Therefore, the loop must pass through the three pearls perpendicular to their line.

Pattern D: White Pearl Diagonal to a Black Pearl

When a white pearl sits diagonally adjacent to a black pearl, the geometry constrains both. The black pearl needs a turn and straight extensions; the white pearl needs straight passage through itself. Together, they often force the loop to route away from the shared corner.

Advanced Techniques

Once the basic patterns are internalized, reach for these advanced weapons.

The Jordan Curve Parity Trick

A closed loop crossing any imaginary line must cross it an even number of times (this is the Jordan Curve Theorem from topology).

How to apply it: Imagine slicing the grid vertically between two columns. The final loop must cross that slice 0, 2, 4, 6... times. If your partial solution has the loop crossing the slice only once so far, it must cross again somewhere — helping you identify where the remaining loop must pass.

Endpoint Counting

As you draw segments, keep track of "loose ends" in each region. Each region must have an even number of endpoints crossing its boundary (again, Jordan Curve). If a region has 3 endpoints trying to escape, you've made a mistake.

Short Circuit Prevention

The most common intermediate mistake: closing a small loop that satisfies nearby pearls but leaves other pearls unreachable. Before connecting two segments, ask: "Does this close the loop? If so, does every pearl lie on this closed loop?" If not — don't connect yet.

Unique Solution Forcing

Published Masyu puzzles have exactly one valid solution. If you reach a branch where both directions seem possible, test each: if one direction allows two completions (violating uniqueness), the other direction is forced. This meta-reasoning is a last resort — proper constraint propagation should solve 95% of puzzles without it.

Solving Strategy Workflow

Here's a reliable order of operations for every Masyu puzzle:

Common Mistakes to Avoid

Even experienced solvers fall into these traps:

Related Puzzles You'll Enjoy

Masyu belongs to a family of loop-drawing Nikoli puzzles. If you love it, try these:

Frequently Asked Questions