MathDB

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?

Problem Statement