A Note On Pigonhole Principle

Abstract:

      Let d. b be fixed positive integers, d1,s₂,…,s_d) is called a game sum sequence if it is a strictly increasing sequence and s_d≤b. Further, if there exist two positive integers m,n(1≤nm -s_n=k or some term s₁=k(1≤i≤d). S is said to have the property k.