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How a solver cracks matrix puzzles

In a Matrix puzzle each cell has four properties: shape, count, shading and rotation. The solver never looks at the cell as a picture. It handles one property at a time.

The method

  1. Split each cell into its four properties.
  2. For one property, look for a pattern in row and column. Each property takes one of three values, so a pattern is "the value moves along by a fixed amount for each step down a row, and by another fixed amount for each step across", wrapping around after three. The solver tries every such pattern (there are 27 per property).
  3. Keep the patterns that match all eight visible cells. If they agree on what the missing ninth cell should be, that is the prediction for the property. A property that never changes has a trivial pattern.
  4. Put the four predictions together and pick the answer option that matches all of them.

This is the same advice the game coaches: decompose the cell, find which properties vary, and track each one on its own.

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