Question 61
$m, n, a, a', b$ and $b'$ are positive integers with $2 \le m \le n$, $a, a' \le m$, $b, b' \le n$ and $(a, b) \ne (a', b')$.
There is a rectangular town like a chessboard with $m$ avenues and $n$ streets. $\langle x, y \rangle$ represents the intersection of the $x$-th avenue from the west and the $y$-th street from the north. For which $(m, n, a, b, a', b')$ there exists a path from $\langle a, b \rangle$ to $\langle a', b' \rangle$ passing all the intersections exactly once?
There is a rectangular town like a chessboard with $m$ avenues and $n$ streets. $\langle x, y \rangle$ represents the intersection of the $x$-th avenue from the west and the $y$-th street from the north. For which $(m, n, a, b, a', b')$ there exists a path from $\langle a, b \rangle$ to $\langle a', b' \rangle$ passing all the intersections exactly once?