The best-known variants are gray pearls (you decide whether each is white or black), toroidal Masyu (the grid wraps around), regional Masyu (the loop must turn in every region) and hexagonal Masyu (played on a hex grid with 60° and 120° turns).
| Variant | What changes | Techniques that still work | New ideas needed |
|---|---|---|---|
| Gray pearls | Some pearls may act as white or black | All loop logic; any pattern that holds for both colours | Case analysis on each gray pearl |
| Toroidal | Opposite edges are connected | Pearl rules, loop logic | No border, so edge and corner openers disappear |
| Regional | The loop must turn at least once in every region | Everything from standard Masyu | Region counting; straight corridors through regions are forbidden |
| Hexagonal | Hex cells; pearls mark specific turn angles | Single-loop logic | New pearl geometry and new parity arguments |
Gray pearls
A gray pearl is a pearl you must classify yourself: in the solution it behaves exactly like a white pearl or exactly like a black one. The loop must still pass through it.
- Start with what both colours share. Either way, the loop visits the cell — so a gray pearl with only two open edges uses both.
- Test the colours. Treat each gray pearl as a small what-if: if “black” forces a contradiction, it’s white, and vice versa.
- Use the border. A gray pearl in a corner must be black, because a white pearl can’t go straight in a corner.
Toroidal Masyu
On a torus, leaving the right edge brings you back on the left, and leaving the top brings you back at the bottom. Every cell is effectively an interior cell, so the familiar corner and edge openers vanish. Solvers rely more on pearl interactions — adjacent black pearls and rows of whites still work — and on careful loose-end tracking, since the loop can wind around the torus in ways impossible on a flat grid.
Regional Masyu
The grid is divided into outlined regions, and the loop must turn at least once inside every region. This adds a new global constraint: the loop must reach every region, and a region it only ever crosses in straight lines is illegal. Small regions become strong clues, because any visit must include a turn — and a black pearl inside a region satisfies it automatically.
Hexagonal Masyu
On a hexagonal grid each cell has six neighbours, so the loop can continue straight or turn by 60° or 120°. Pearls mark which kind of turn happens, which changes nearly every local pattern. The global loop rules — no branches, no premature loops, even crossings — still apply.
Why try variants?
Variants expose which of your techniques are really about Masyu’s rules and which are just habits. Playing a toroidal puzzle, for example, shows how much you lean on the border. Coming back to standard Masyu afterwards, many solvers find interior deductions much easier to spot.
All puzzles on MasyuPuzzles.com use standard Masyu rules. Variant descriptions follow common usage in the puzzle community; individual setters sometimes define details differently, so always read a variant puzzle’s own rules.