Come now everyone, can't you recognize a lovely puzzle when you see it? This can be achieved with 6 T flip-flops (unless I've made an error, but I bet 7 tops), assuming those flip flops have complementary outputs. No steering diodes or the like and certainly not a Rube Goldberg solution.
However, I have to agree with edavid, this is very obviously a problem created with a solution in mind. Hence, I'm sitting on my solution until we see some working/thoughts from the OP.