Around the World
A friend offers this interesting variant of your logistics puzzle:
You are commander of an aircraft carrier near the equator. Your
mission is to send a single plane around the equator, taking off
from and landing on your own ship.
That plane is one of a large number of specially designed tankers
that holds enough fuel to travel 1/5 of the distance around the
world. These tanker planes can transfer unlimited amounts of
fuel between each other (in flight) in virtually no time, provided
the planes in question are in the same location. Takeoffs and
landings require virtually no time. An effectively infinite
amount of fuel is available on the carrier, and refuelings on
the ship take virtually no time. The planes are designed such
that there is no distinction between their cargos and their own
fuel supplies. All planes travel at the same speed regardless
of weight (fuel) status, and consume fuel at the same rate.
You may launch as many planes as you like before, during, and
after the flight of the one plane in question which must
circumnavigate the globe. All planes must be safely recovered,
meaning they must be landed back on the ship before running out
of fuel. You are not permitted to land planes, even temporarily,
anywhere else in the world, nor may you deposit fuel anywhere
else in the world for later retrieval (if necessary, you may
jettison unwanted fuel over any location). Planes are permitted
to circle a location but continue to consume fuel at the same rate.
There is no limit to the number of planes which may be present
at a single location at one time.
What is the minimum number of planes required to complete the
mission, and how? (This would be the same as the maximum
number of planes in the air during the course of the
mission.)
Note: although no proof is known that any particular solution
is minimal, solutions are known with fewer than 80 planes.
Sorry, I am unable to post such a solution. My friend
showed me a solution requiring more than 100 planes that looked
feasible, but it would require a drawing to be comprehensible.
Hint (backwards): tsaeehtotdnatsewehtothtobsenalphcnualyamuoy |
