John and Peter play the following game using a regular chessboard. John thinks of 8 squares so that no two squares lie in the same row or in the same...
Suppose that $QQ'>PP'$. Drop perpendiculars $PR$ and $P'R'$ on $QQ'$. Let $M$ and $N$ be the midpoints of $PP'$ and $QQ'$, respectively. Then $PRNM$...