Puzzle #7 - Transitions - Solution

This one was solved pretty quickly. Basically I was trying to trick you. The idea was to try to create the impression an infinite amount of memory is necessary to hold all the 0–>1 and 1–>0 transitions. In practice there cannot be 2 consecutive 0–>1 transitions (or vice versa) since if the input goes from 0 to 1 before the next 0–>1 transition it must change to a 0 and thus have a 1–>0 transition!
The FSM can have only three states: “exactly one more 0–>1″, “equal amount of 0–>1 and 1–>0″ or “exactly one more 1–>0″.