Question 108
A function $f$ satisfies, for all nonnegative integers $x$ and $y$:
- $f(0, x) = f(x, 0) = x$
- If $x \geq y \geq 0$, $f(x, y) = f(x - y, y) + 1$
- If $y \geq x \geq 0$, $f(x, y) = f(x, y - x) + 1$
Find the maximum value of $f$ over $0 \leq x, y \leq 100$.
- $f(0, x) = f(x, 0) = x$
- If $x \geq y \geq 0$, $f(x, y) = f(x - y, y) + 1$
- If $y \geq x \geq 0$, $f(x, y) = f(x, y - x) + 1$
Find the maximum value of $f$ over $0 \leq x, y \leq 100$.