How to Solve Masyu: Rules, Circle Logic, and Beginner Strategies

Masyu is a loop puzzle built on two rules: white circles must be passed through in a straight line (but the loop turns in a neighboring cell), and black circles must be turned at (but the loop runs straight through both neighbors). Draw one continuous loop through every circle, and you have solved it.

What Is Masyu?

You see a grid, you see circles — some white, some black — and the instruction says “draw a loop.” That description does not immediately suggest why the puzzle is challenging. The challenge comes from keeping two distinct circle rules straight in your head while tracking a loop that must stay connected from start to finish.

Masyu was created and published by Nikoli. It first appeared in Puzzle Communication Nikoli #84 under the name “Shinju no Kubikazari” (真珠の首飾り — “pearl necklace”), featuring white circles only. Black circles arrived in issue #90, when the puzzle was renamed “Shiroshinju Kuroshinju” (白真珠黒真珠 — “white pearls and black pearls”). The current name “Masyu” was adopted in issue #103. The origin of that name is one of the more memorable facts in puzzle history: Nikoli’s president had misread the kanji 真珠 (shinju), the mistake turned into an in-house joke, and the joke became the official name.

If you have spent time with other loop puzzles, Slitherlink is the closest relative — it also asks you to draw one closed loop across a grid. The mechanisms are different (Slitherlink uses numeric clues at cells rather than circles inside them), but the instinct of tracking one unbroken path is the same.

The Rules of Masyu

Three facts, then two circle rules. Understand those five things and you understand the entire puzzle.

The loop. The solution is a single continuous, non-intersecting loop that passes through every circled cell on the grid. The loop enters each cell through one side and exits through a different side. Every turn is exactly 90 degrees.

White circles. The loop passes straight through a white circle — it cannot turn at that cell. However, the loop must turn in at least one of the cells directly before or after the white circle in its path.

Black circles. The loop turns at a black circle — it cannot go straight through. However, the loop must travel straight through both the cell directly before and the cell directly after the black circle.

💡 Quick memory anchor

With a white circle, the circle is the straight move and its neighbors do the turning. With a black circle, the circle is the turning move and its neighbors stay straight.

The rules are easy to say and surprisingly easy to swap. A useful memory anchor: white = straight at the circle, turn in a neighbor. Black = turn at the circle, straight in both neighbors. Flipping those two by accident is the most common beginner error — and it is easy to do mid-puzzle when attention drifts.

Figure 1. The loop goes straight through the white circle. It is the cell next to it that must turn.

Figure 2. The loop turns at the black circle cell. The cells directly before and after it must stay straight.

Step-by-Step: Solving Your First Masyu

Starting a Masyu puzzle from scratch is manageable when you work in a deliberate order. Here is a reliable sequence for beginner-level grids.

Identify every black circle before drawing anything. Black circles force a 90-degree turn — the direction options are limited, and they constrain the cells on either side as well. A light pencil mark showing the turn direction helps.
Start at the outer border and work inward. Circles near the edge of the grid have fewer exit directions available. A black circle touching the border, for example, can only turn toward the center of the grid. Forced moves near the edges reveal segments quickly.
Resolve adjacent black circle pairs first. When two black circles sit next to each other, the loop cannot run directly between them — if it did, the other black circle would have to be straight at the same time it must turn, an immediate contradiction. The loop must extend away from each circle instead, which forces several segments at once.
Use the straight-constraint of black circles to rule out segments nearby. After the loop turns at a black circle, the next cell must be straight. Any segment that would force a turn in that cell is ruled out — mark it with an X.
Return to the white circles with what you have placed. With some segments already drawn, you can often determine the direction the loop travels through each white circle. Check whether a neighbor already contains a turn: if so, the remaining direction through the white circle is confirmed.
Let X marks do the work. As ruled-out segments accumulate, remaining options narrow. For any circled cell, once two of its four sides are ruled out, the remaining two must both be segments. Each new X mark reduces choices for neighboring cells; this cascade of constraints, not guessing, drives Masyu to its solution.

If you reach a contradiction — a circled cell with no valid way for the loop to enter and exit — retrace your steps to the last point where a choice existed and try the other direction.

Masyu Strategies That Actually Help

Start at the border, work inward. Grid edges act as invisible walls, restricting loop directions. Border circles — and especially corner circles — have fewer valid path options, which makes forced moves easier to see. White circles at the edge are particularly fast to resolve: the loop must pass straight through them, and with the grid’s border right there, the direction of that straight path is often forced immediately. As puzzle-magazine.com’s Masyu solving tips note, edge white circles typically have only one valid direction and can be marked right away. Tackle border circles before working into the center.

Count your straight cells after each black circle. Both neighbors of a black circle must be straight. That means the loop cannot turn again in the cell directly after a black circle. This constraint often eliminates segment options two or three cells away from the circle itself, clearing space faster than it appears.

Adjacent black circle pairs are an efficient early move. Two black circles directly next to each other cannot share a connecting segment — placing one would force the second black circle to be straight at the same time it must turn, an immediate contradiction. The loop must extend outward from each circle. Resolving these pairs early often unlocks a long chain of forced segments through the rest of the grid.

For what it is worth as context: according to Erich Friedman’s paper “Pearl Puzzles are NP-complete”, solving Masyu on arbitrarily large grids belongs to the class of NP-complete problems — meaning the difficulty can scale steeply as grids grow. Puzzles in books and apps are designed to have a unique logical solution; the math is a reminder that the complexity you feel in harder grids is real.

✓ The three fastest openings

Border and corner circles: fewest valid directions, so forced moves appear first.
After a black circle turns: the next cell must stay straight — rule out anything that would turn.
Adjacent black circle pairs: no segment can sit between them, so the loop extends outward from each.

Common Mistakes

Treating the white circle as a free pass. The loop must go straight through the white circle — that part is correct and fixed. What beginners overlook is that at least one of the neighboring cells must compensate with a turn. Placing a straight-through path and then drawing more straight segments on both sides of the white circle violates the rule.

Treating the black circle as a turn-only decision. Yes, the loop turns at a black circle — but it must also travel straight through the cells on either side. Turning correctly at the circle and then turning again one cell later is a common error that is easy to miss when the loop is half-drawn.

Building more than one loop. The solution requires exactly one continuous loop that covers every circle. If segments on one part of the grid close into a small ring before the rest of the circles are resolved, the puzzle is broken. Watch for any segment that would complete a partial closure too early.

Skipping circles. Blank cells may or may not have the loop passing through them — they carry no constraint either way. But every white or black circled cell must be visited by the loop. A solution that bypasses even one circle is incorrect.

Practice

If you enjoy logic puzzles with a clear rule set and a satisfying logical solution, a few other Nikoli formats in this series are worth trying: how to solve Nurikabe, how to solve Hitori, and how to solve Suguru each have a compact rule set and a unique solving rhythm. For offline practice, Make10s printable worksheets offer paper-based number puzzles if you prefer working away from a screen.

For something different between sessions, Make 10 is a quick number puzzle — you connect tiles so a run of touching numbers adds up to ten. No download, no account, plays in your browser in under a minute.

10 Try Make 10 ↓ A free number puzzle — no app, no sign-up. Connect tiles so a run of touching numbers adds up to ten. Play now →

Frequently Asked Questions

What do the white and black circles mean in Masyu?

White and black circles are the only two clue types in Masyu. The loop must pass straight through a white circle, with at least one neighboring cell containing a turn. The loop must turn at a black circle, with both neighboring cells running straight.

Is Masyu hard for beginners?

The rules fit in two sentences. The challenge is applying both circle rules simultaneously without swapping them mid-puzzle. Starting with small grids and focusing on border circles and adjacent black-circle pairs makes the early learning curve much gentler — most beginners find the rules click within a few solved puzzles.

Is Masyu the same as Slitherlink?

No. Both are loop puzzles built on a grid, but the mechanics differ. Slitherlink uses numeric clues at each cell to count how many of that cell’s edges the loop uses. Masyu uses white and black circles to control whether the loop turns or goes straight at each visited cell. If you enjoy one, how to solve Slitherlink is a natural next step — it shares the same “one loop, all logic” structure.

Where can I play Masyu for free?

Krazydad.com has a large archive of Masyu puzzles at a range of difficulty levels, available in both printable and interactive formats.

Sources: Wikipedia — Masyu · Erich Friedman — “Pearl Puzzles are NP-complete” · puzzle-magazine.com — Masyu Solving Tips

Just for fun — not medical advice.

About the author: Jay M. spent years in private education — including managing a coding academy branch and creating online educational content — before building Make10s as a free resource for adults who want to keep their minds active and engaged. The games and guides here are designed to be genuinely useful, not just eye-catching.