1. The problem statement, all variables and given/known data Find a one-to-one correspondence between the binary strings (i.e. sequences of 0's and 1's) of length k that have an odd number of 1's, and those that have an even number of 1's. 2. Relevant equations 3. The attempt at a solution I'm not exactly sure of what it's asking me to do. If it's of length k, then you have 2^k different combinations. Half of these will have an even number of 1's, half will have an odd number. So you get (2^k)/2 or 2^(k-1) with an odd number of 1's, and 2^(k-1) with an even number of 1's. Not exactly sure where to go from here.