A tile is one of the two triangles made by cutting a square of area in half along the diagonal.
In attempting to tile a by square floor using these tiles with none of them overlapping and none going outside the square, it is impossible to tile it fully.
Find the maximum number of these tiles which can be used in this tiling.
Demonstrate how to do this and prove that no more tiles will fit.
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Cayley Mathematical Olympiad (2025)
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