You can actually transmit this information in a single bit: just have your friend send a 0 if you should answer false on everything or 1 if you should answer true on everything. To use the other 11 bits, transmit the first 11 answers first, and then encode whether to guess true or false on all of the remaining 12 questions in the last bit. This method gives 11 + (23-11)/2 = 17 answers correct in the worst case, but (according to the author) this is still suboptimal.