G
remmie’s
F
un
P
ages
edited by Gerald Muus
Solution to Last Issue’s Brain Teaser:
In the previous issue, we had to fly a doomsday bomb completely around the world in order to
defuse it. Our planes are all identical, and capable of refueling each other in flight.The planes
must all take off and land safely from the one remaining habitable island in the world. We have
an unlimited supply of aircraft and fuel on the island.The challenge is to determine the minimum
number of planes that we would need to use in order to accomplish this. (Assume no time needs
to be allowed for takeoffs, landings, and refueling).
The trap that most people fell into was in confusing the relationship between distance traveled and
fuel used. It is important to remember that ¼ of the trip around the globe uses ½ a tank of fuel.
Another pitfall was in forgetting that any plane that refueled another needed to retain enough fuel
in reserve in order to reach the home island safely.
The trick is to find a way to give the plane carrying the bomb a full tank of fuel at the point at
which it has burned half of its fuel, which is at ¼ of the way around the world.That fuel will carry
it to the ¾ mark before it will need to be refueled.
The solution is to divide the trip around the Earth into 8 segments. Plane “A”, which is carrying
As Assistant Editor of
Discover Smith Mountain
Lake, “Gremmie” loves
to get mail. Here she is,
busy at work, looking over
the entries in our puzzle
competition.
If you care to drop her a
line, send it to:
Gremlin the Wonder Cat
Assistant Editor
Discover Smith Mountain
Lake Magazine
P.O. Box 880
Moneta, VA 24121
Or via e-mail at:
gremmie@discoversmith-
mountainlake.com
the bomb, takes off with a full tank of fuel, accompanied by
Planes “B” and “C”, also fully fueled. At the 1/8 mark, all
three planes have ¾ tank of fuel. If “C” wants to return safely,
he can transfer up to ½ tank of his remaining fuel, leaving
him with ¼ tank, which will take him safely home. So at
the 1/8 mark, “C” gives “A” and “B” each ¼ tank of fuel and
returns to the island.
The other two planes continue on to the ¼ mark. At this
point, again, each has ¾ of a tank of fuel remaining. “B” now
needs ½ tank to get back home safely, so he transfers the
remaining ¼ tank to “A”, who now once again has a full tank.
“
A” now continues on his journey around the world, with
enough fuel to carry him to the ¾ mark. In the meantime,
“
B” and “C” have returned safely to the island, and refueled.
“
B” immediately takes off in the opposite direction around
the world to “A”. When “B” has reached a point ¼ of the way
around, he will meet up with “A”, coming from the other
direction. At this point, “B” will have ½ tank of fuel, and “A”
will be on fumes.
“
B” then gives half of his remaining fuel, or ¼ tank, to
“
A”, and joins him on his route back to the island. At that
moment, “C” has taken off on a course to join them at the 7/8
point on the circumnavigation. When “C” intercepts “A” and
“
B”, they are both running on empty. “C” now has ¾ of a tank
of fuel, and gives ¼ tank each to “A” and “B”.This gives all of
them just enough fuel to reach the island safely.
Since we accomplished our mission with 3 aircraft, and
it would have been impossible to do so with 2 planes,
the minimum number of planes required to successfully
accomplish our mission is “3”.
Congratulations to Jeff Aldrich, who was
the first to submit the correct solution to this
challenge. We were fairly impressed with his
skill at illustrating his solution as well!
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Discover Smith Mountain Lake | Spring 2013
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