Two engines are designed to be parachuted to the random points of the infinite straight railway. After landing, they face in the same direction on the track (either forwards or backwards).
The engines operate automatically by the on-board computer with a single absolutely identical program inside each computer.
The engines both discard their parachutes at the point of landing, and then their control programs start.
The computer can recognize the following 4 commands:
FORWARD- Move one step forward.BACKWARD- Move one step backward.GOTO <label>- Switch control to the command marked by<label>(each command may have a unique label).IF (CHUTE) THEN <command>- If there is a parachute at that point, execute<command>(any command described above). The engines cannot recognize if the parachute is their own.
You are the programmer of the engine on-board computer. Your goal is to make two engines crash. Can you do that?
Use the following program:
go:
FORWARD
IF(CHUTE) THEN GOTO run
BACKWARD
FORWARD
GOTO go
run:
FORWARD
GOTO run
Proof
First note that the engines always travel forwards overall. Since they are both
facing the same direction they will continue going forward (in the go
loop) at the same speed until the one who is following finds the parachute of
the other. It will then start moving at a faster speed than the first (in the
run loop), as it no longer has to do a BACKWARD FORWARD every
iteration. Thus it will eventually catch the first.