Mosaic

Draw a mosaic consisting of half-coloured cells and empty cells.

Each cell must be either empty, or half-filled by a triangle, in such a way that the empty regions form only rectangles. Cells with numbers indicate how many rectangles are adjacent to that cell.

Example

In this example, the top right cell is not adjacent to any rectangles, so there must be two triangles adjacent to it. These must be the top right triangles of their cells, otherwise the empty halves of these cells couldn't become rectangles anymore. Now, the two diagonal sides of these triangles must be the side of a rectangle, and there is only one way to complete this rectangle.

The cell in the bottom right needs one rectangle. Since it cannot be at the top anymore, it needs to be to the left. If this rectangle would be more than one cell big, the cell above it could not be filled anymore, since it already has triangles on two sides. So, the bottom rectangle stops after one cell, and the bottom left four cells must form a diagonal square. Finally, the number 1 in the top left needs one rectangle, which is the remaining cell in the top left.

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Alternative name: shakashaka.

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