Puzzles
1 December
One of the vertices of a rectangle is at the point \((9, 0)\). The \(x\)-axis and \(y\)-axis are both lines of symmetry of the rectangle.
What is the area of the rectangle?
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The only way this is possible is if the rectangle is this square:
The area of this square is 162.
Placing plates
Two players take turns placing identical plates on a square table. The player who is first to be unable to place a plate loses. Which player wins?
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The first player can always win by first placing a plate on the exact centre of the table. Then the first player can copy what the second player does, but rotated 180°, and hence can always place a plate if the second player could.
Extension
What if the two players play on a regular hexagonal table? Or a regular octagonal table? Or a regular pentagonal table? Or a regular \(n\)-gonal table?
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