Put four black squares into an 8x8 grid, such that the remaining white squares can be connected in only one way in a closed loop, visiting each white square exactly once (moving only up, down, right, or left.) One example is above; only one closed loop can connect all the white squares. How many different arrangements of four squares can determine a unique path?
Source: Original extension of previous 5x5 puzzle. To compare solutions, rotate/reflect your grid to put each black square as close to the top left as possible.