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?

On December 8, 2019 I competited at ACM ICPC Kharagpur Regionals 2019-20. My team was able to solve only 2 problems. Except those we were at the end to finish more 3 problems. But as we weren't able to optimise a formula of Combination (in the Chef and Diamond problem) and some other implementation problems(for other 2 problems) we weren't able to solve any of three.Can anyone guide me from where and how can I prepare for having a good command on mathematics for programming. Also mention some good sites or books to prepare.