Challenge: Knight Expected Moves

Instead of probability, find the expected number of moves before the knight leaves the board. Let $E[r][c]$ = expected moves from $(r, c)$. If on board: $E[r][c] = 1 + \frac{1}{8} \sum E[next]$ where $next$ are valid destinations. Off-board destinations contribute 0 (no future moves).

This creates a system of equations. Solve iteratively: initialize all $E = 0$, then update until convergence. Or use Gaussian elimination for exact solution.