Find a closed path through a 10x10 board visiting each square one and only time and following these rules: skip two squares moving up, down, left or right and skip only one square moving diagonally (that's a hamiltonian cycle).

Here you have a solution (it changes if you reload this page!). In order to lower the computational cost, the algorithm starts filling the first 5x5 quadrant and then goes on in a symmetrical way.