Two robots are to be parachuted onto random locations on an infinite line. When they land, their parachutes detach and remain where they are. The robots may each be programmed with numbered instructions from the following set:

• Go left one unit
• Go right one unit
• Skip next instruction unless there is a parachute here
• Go to (label)

Each instruction takes one cycle to execute. Program the robots to collide.

Notes:

There must be a finite number of lines of code (ie, you can't say move right once, then left twice, then right thrice, .. ad infinitum).
Try to do it using the fewest lines of instructions (if both robots have the same instruction set, you can count it only once).
There is no way for the robots to distinguish between the two parachutes if they are crossed.

The instructions in the program are numbered, and are executed in order. An instruction of "go to" some label means that the next instruction to follow will be at that number, and continue from that point in numerical order.
For example, look at the following:

10  right one unit
20  left one unit
30  go to 10
40  do a backflip

This code would have the robot forever going back and forth between two spots.
Line 10 would execute, then 20, then 30, and then back to 10 (line 40 in this example would never be run).

(In reply to Two robots, same program by Brian Smith)

My own solution to the problem had been the same as Brian Smith's (except right and left reversed), but had been based on misreading the problem. However, it does form a solution to a variation of the problem. The variant is, assume that the time taken to process instructions is negligible, and in fact can be done in parallel to the actual motion, so that only the MOVE instructions take a unit of time, because the robot has to actually move mechanically. Brian's (and my own) solutions slow the robot down under these circumstances also.

Posted by Charlie on 2003-09-12 09:41:56