There is a very popular kid toy called Hungarian Rings ( https://f-droid.org/en/packages/eu.veldsoft.hungarian.rings/ ). You must recover the initial state by moving the puzzle pieces in such toys. Universal combinatorial formulas for solving the Hungarian Rings are very well known. I would like to ask you how such formulas can be found. I am asking because there is another puzzle called Fish Rings ( https://f-droid.org/en/packages/eu.veldsoft.fish.rings/ ), and it does not have a universal formula published. I would like to search for them.