2016 IMO Shortlist C1

The leader of an IMO team chooses positive integers $n$ and $k$ with $n>k$, and announces them to the deputy leader and a contestant. The leader then secretly tells the deputy leader an $n$-digit binary string, and the deputy leader writes down all $n$-digit binary strings which differ from the leader's in exactly $k$ positions. (For example, if $n=3$ and $k=1$, and if the leader chooses 101, the deputy leader would write down 001, 111 and 100.) The contestant is allowed to look at the strings written by the deputy leader and guess the leader's string. What is the minimum number of guesses (in terms of $n$ and $k$ ) needed to guarantee the correct answer?

IMO 团队的领队选择正整数 $n$ 和 $k$(其中 $n>k$)，并将其宣布给副领队和参赛者。然后，领导者秘密地告诉副领导者一个 $n$ 位的二进制字符串，副领导者写下所有与领导者的 $k$ 个位置不同的 $n$ 位二进制字符串。 (例如，如果$n=3$且$k=1$，如果组长选择101，则副组长将写下001、111和100。)允许参赛者查看副组长写的字符串并猜测组长的字符串。保证正确答案所需的最少猜测次数是多少(以 $n$ 和 $k$ 计)？