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wikiHow to Solve a Masyu Puzzle

Masyu is a type of puzzle in which the solver is presented with a rectangular grid with black and white circles. The objective is to find a closed loop subject to the following constraints:

  • The loop must pass through each black circle making a right angle and must continue straight for at least one additional square before and after the turn.
  • The loop must pass straight through each white circle, but must make a 90 degree turn immediately before and/or immediately after passing through a white circle.
  • There must be a single closed loop and it cannot pass through the same square twice.


  1. 1
    Look for any of these local conditions and draw the appropriate inferences:
    • A black circle on the edge or one square away from the edge must extend toward the center.
    • Two adjacent black circles must move away from each other.
    • A white circle on the outer border must go parallel to the border. If two white circles on the border are adjacent or have only one space between them, both must turn inward after they connect.
    • Three or more consecutive white circles force the path to pass through them separately as shown. The path cannot pass straight through all of them without violating the turn constraint of the middle one.
    • A black circle diagonally adjacent to two white circles in the same row or column must move away from them. More generally, the path through a black circle cannot make a corner around any white circle.
  2. 2
    Reapply the above conditions again and after any significant progress. Each additional segment of the path that is known adds more boundary to the unsolved portion. The new segments created an edge near a white circle and a black circle restricting the way the path must pass through those cells.
  3. 3
    Look at the endpoints of each segment of the path. Consider which direction it could take next, straight, left turn, or right turn. If only one continuation exists, take it. Avoid all of the following situations:
    • Intersecting another part of the path. Do not create any 3 or 4-way junctions.
    • Forming a closed loop that is smaller than the complete solution. There must be only one loop.
    • Creating a closed off region that contains an odd number of endpoints. This will create a string, but there will be no way to connect the loose ends to close the loop.
    • Violating a turn constraint.
  4. 4
    A white circle two cells away from a black circle can impose a restriction since it the path extends from the black circle to the white circle it is forced to immediately turn. If this is not possible, then the path from the black circle must extend in the opposite direction.
  5. 5
    Look for any region that is almost closed off from the rest of the puzzle. Any isolated region must contain an even number of endpoints.
  6. 6
    Continue to look for obstructions similar to those above created by the new parts of the path drawn. For example, if any part of the loop passes parallel to and adjacent a white circle, then you must pass through the white circle in the same direction to avoid creating a 3-way junction.
  7. 7
    As most of the solution gets filled in, switch from thinking locally to thinking globally. Getting a good start requires local observations like those described in step one. Finishing the puzzle requires focus on avoiding small loops and dead ends.

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    • If you know the puzzle is intended to have a unique solution, sometimes this can be used to help. If connecting one way would lead to multiple solutions, then connect the other way. This could have been applied to the four isolated endpoints in the upper right in step 5. There are three ways to connect them horizontally without affecting any other part of the puzzle, but only one way to connect them vertically. The risk in using this is that if a puzzle does have multiple solutions, this assumption may lead you to miss all of them.

    Things You'll Need

    • Masyu puzzles
    • Pencil
    • Good eraser

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