title: could not prove dynamic programming requirements
body: <p>I am not able to prove the optimal substructure and overlapping subproblem property for the problem in the <a href="https://www.hackerrank.com/challenges/play-game" rel="nofollow">link</a>.
  The exact problem with me is that even after understanding standard problems of dp , i face problem in approaching the newer problems. Sometimes i can't find the subproblems of the solutions and sometimes i cannot prove the correctness of my approach to the problem. :</p>