I first saw this question on the usenet group sci.math many years ago,
but see below for what I believe is its true origin.
This is allegedly a true story.
Early in the Cold War the Soviet Union sought to defend its bombers by fitting
rearward* firing missiles**
Every time this was tried the missile would make an immediate U-turn and hit
the aircraft that fired it. Why was this?
*At that time the best position from which to attack a bomber was from
behind, as less/no deflection or lead was needed on unguided weapons, and
early Infra-Red homing missiles needed to see the hot exhaust to lock-on.
Also this is the easiest intercept geometry when using Ground Controlled
**One source quotes missile in the singular, I would have thought it more
likely that they tried multiple fin or spin stabilised unguided rockets, which
were a common air-to-air weapon at the time.
(Paraphrased form "The Chicken From Minsk" by Chernyak and Rose, with
comments added by CaptainBlack).