Knight's Tour recursion

Question

Is anyone able to find a mistake in my knight's tour code? I can't seem to find it, and I'm getting an infinite loop, not a stack overflow

private bool heuristic(int[,] board, int x, int y, ref int jmp)
{
    if (x < 0 || x > 7 || y < 0 || y > 7 || board[x, y] > 0)
        return false;
    board[x, y] = ++jmp;
    if (jmp == 64)
        return true;

    if (heuristic(board, x + 2, y + 1, ref jmp) ||
        heuristic(board, x + 2, y - 1, ref jmp) || heuristic(board, x - 2, y + 1, ref jmp) ||
        heuristic(board, x - 2, y - 1, ref jmp) || heuristic(board, x + 1, y + 2, ref jmp) ||
        heuristic(board, x + 1, y - 2, ref jmp) || heuristic(board, x - 1, y + 2, ref jmp) ||
        heuristic(board, x - 1, y - 2, ref jmp))
        return true;
    board[x, y] = 0;
    jmp--;
    return false;
}

And calling it:

var board = new int[8,8];
var x = 0;
var y = 0;
var jmp = 0;
var result = heuristic(board, x, y, ref jmp);

I need to have a jmp variable as I'm preforming multiple trials and also want to show the path taken. Thanks!

Answer 1

According to Wikipedia:

There are 26,534,728,821,064 [...] tours

and

A brute-force search for a knight's tour is impractical on all but the smallest boards; for example, on an 8x8 board there are approximately 4×10⁵¹ possible move sequences, and it is well beyond the capacity of modern computers (or networks of computers) to perform operations on such a large set. However, the size of this number gives a misleading impression of the difficulty of the problem, which can be solved "by using human insight and ingenuity ... without much difficulty."