in the robot room in castle of dr. brain there are three robot heads. you need to program each of them to fetch some items in a small maze. the problem is that not all of the robot heads work correct all the time.
there is more information one can get by spending one hint coin or by trial and error: one robot always does as told, one robot always does the opposite of what it is told, one robot head alternates between correct and opposite.
here is what the three robot heads say about themselves:
propeller head: "I am programmed to always follow instructions precisely. Iron Face also follows instructions precisely"
saucer head: "I am programmed to always follow instructions precisely. I am the only precise order-follower here."
iron face: "I am programmed to always follow instructions precisely. Saucer Head never follows orders correctly."
i figured this out when i played this game as a child, and i figured it out again now. but somehow i don't feel satisfied because my method of solving the puzzle is by some combination of backtracking and trial and error. i know from my logic class (years ago) that one can deduce the solution somehow, but i fail to do so.
can someone provide me with a formal logical approach to solve this puzzle.
note: i am not interested in only the solution. i know that already.