A cross-shaped window shows a cell's four neighbours, but not the cell. Can every cell of a 4×4 torus look different through it? Game 1: find two cells with the same cross. Game 2: paint your own grid and watch the collision appear.
First pick
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Second pick
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Pick two cells whose crosses read the same.
This grid has 12 distinct cross readings across its 16 cells.
Faded cells are the far side of the torus: an arm that leaves the grid comes back in from the opposite edge. Read a cross as up left right down.