I agree with you. I agree with OP in the following sentences: >We have now landed on our final strategy: start by figuring out the number of possible secret co

I agree with you. I agree with OP in the following sentences: >We have now landed on our final strategy: start by figuring out the number of possible secret codes n. For each guess, calculate the number n_i' of codes that will still be viable if the Code Master gives response i in return. Do this for all possible responses. But then I don't agree with: >Finally, calculate the entropy of each guess; pick the one with the highest. Why wouldn't we just pick argmin_{guess} sum{i in possible responses}{Pr[i] * n'_i} = sum{i in possible responses}{n'_i/n * n'_i} = sum{i in possible responses}{n'_i^2}? This is the guess that minimizes the expected size of the resulting solution space.