Wednesday, August 8, 2018

Paratroopers Puzzle


Two paratroopers are dropped onto a practically infinite railway track. Both were given a note with the identical instructions... They both follow the instructions and eventually meet up.
What did the note tell them to do.


To drop their para-shoots on the track. Then they should run north 10 steps then switch and run 3 times to the south and switch again and triple and do not stop until they meet or reach the other parachute...

The fun answer:

The standard random walk has the properties related to the normal distribution (which Bernoulli approximates as N approaches infinity). For the random walk the mean position for the random walker is his or her starting point. The variance however grows with the root of the time. So pretty much any random walk would work as a rendezvous strategy - whenever they run past a pub, pop in and do not leave until you are punch drunk is probably as good randomising strategy for the above answer.

For more details you can look at the following entry on Cross Validated.
This is also called the two robots problem.