Is there a way to calculate periodicity of subtraction games with any given set of numbers? Or atleast any calculation which tells the periodicity will be less than a particular value!
For example: For subtraction Set {1, 3, 4}, the nim sequence will be: 0,1,0,1,2,3,1,0,1,0,1,2,3,1,0,1,0,1,2,3..... Here the period is 7.
So for any given subtraction set, is there any method to calculate the period of its nim sequence?
This paper could be helpful: The Period of the subtraction games, Zhihui Qin, Guanglei He
Not completely, but yeah it was helpful with the special cases mentioned in the paper. I think there is no general formula for this, just for some type of cases and observation, calculations are given. Anyways... Thanks :)