We propose hysteresis neural network solving combinatorial optimization problems, Box Puzzling Problem. Hysteresis neural network searches solutions of the problem with nonlinear dynamics. The output vector becomes stable only when it corresponds with a solution. This system does never become stable without satisfying constraints of the problem. After estimating hardware calculating time, we obtain that numerical calculating time increases extremely comparing with hardware time as problem's scale increases. However the system has possibility of limit cycle. Though it is very hard to remove limit cycle completely, we propose some methods to remove this phenomenon.