Problems(1)
Let k≥4 be an integer. Sunny and Ming play a game with strings. A string is a sequence that every element of it is an integer between 1 and k, inclusive. At first, Sunny chooses two positive integers N,L≥2 and write down N strings, each having length L. Then Ming mark at most 2N strings. Then Sunny chooses an unmarked string s and calculate the biggest integer n such that there exists another string satisfying its first n element is the same as the first n element of s. Then Sunny burn down all strings which first n element if different from the first n element of s, leaving only the ones which have the same first n element of s. Finally, Ming chooses an integer d between 1 and k, inclusive, and remove all strings which (n+1)th element is d. Sunny's score would be the number of strings left. Find the maximum score that Sunny can guarantee to get.Proposed by USJL combinatoricsIMOC