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Free printable Masyu with answers

Masyu is a loop puzzle: draw one closed loop through the centres of cells so it runs straight through every white circle and turns on every black one. Two rules, a lot of consequence, and exactly one loop every time.

By size

Two things make a Masyu harder: a bigger board, and fewer circles on it. The grades move both together, so start small and work up.

By audience

There are only two rules and the answer is a drawing rather than a filled grid, which is why this one suits children and new solvers better than most logic puzzles.

One loop, every time

This is the guarantee that is hard to make in this genre, and the reason most free Masyu puzzles are not worth printing. A board can satisfy every circle and still be drawn as two separate rings, which is not an answer at all. Every puzzle here is built so its answer is a single closed loop, then proved by the same solver our Publisher Studio uses. The answer prints at the back.

How to solve a masyu

Draw one closed loop through the centres of cells so it runs straight through every white circle and turns on every black one. Cells with no circle are free, and the loop need not visit them.

The method

  1. 1Start with the circles on the edge. A white circle in the top or bottom row has no vertical option, so the loop must run across it; one in the left or right column must run down it. A black circle near an edge can only send that leg inward, and it has to reach two cells, which fixes a surprising amount for free.
  2. 2Extend every black circle two cells. The loop turns on a black and then runs straight for a full cell on both sides, so each black gives you three segments at once as soon as you know which way it turns. Two blacks a single cell apart can never both point at each other.
  3. 3Look for whites in a row. A run of white circles in a line all go straight, so the loop crosses the whole run. The turn each one needs has to happen at one end or the other, which often decides the end of the run.
  4. 4Remember a white's turn is close. A white is not just a straight. It also promises a corner within one cell on at least one side, so a white in the middle of a long straight run is impossible. That rules out more lines than it looks like.
  5. 5Refuse the early loop. If closing a line would make a small ring while any circle is still off it, that closure is wrong. There is only one loop in the finished puzzle, and every circle is on it.
The one rule
One closed loop through cell centres, no branches and no crossings, straight through every white circle and turning on every black one.
What the answer page shows
The finished loop is printed at the back.
How the grades differ
Harder grades are bigger boards with fewer circles, so longer stretches of the loop come from the degree rule rather than from a circle.
Good for
Solvers who like a puzzle with two rules and a lot of consequence.

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