Juggling in a Raft
Marilyn is Wrong Copyright © 1997-1998 Herb Weiner. All rights reserved.
Ask Marilyn ® by Marilyn vos Savant is a column in Parade Magazine,
published by PARADE, 711 Third Avenue, New York, NY 10017, USA.
According to Parade, Marilyn vos Savant is listed in the
"Guinness Book of World Records Hall of Fame" for "Highest IQ."
Fred Moolten <firstname.lastname@example.org>
remembers the following Marilyn column.
If you have this column, please send it to me.
A reader asked how a person could transport three balls
across a river on a raft that could sustain a maximum weight of
the traveller plus two of the balls. Marilyn assumed that multiple
crossings were not permitted, although the puzzle did not state this.
To her credit, this assumption converted an easy problem into a
Marilyn considered a clever approach to the challenge:
reduce the force of the balls on the raft.
In considering how this might be done, she mentioned juggling the balls
so that the traveller was not holding them all at once.
She then explained that this would not work because the impact of a
second ball descending into the hand of a juggler already holding one
would bring the total downward force beyond the limits of buoyancy.
Although Marilyn did not discuss juggling all three balls so that
there are always at least two in the air at a time, this would not work either.
The problem with juggling as a
solution does not depend on any need to handle two balls at once.
Rather, for three balls to end a long journey at the same altitude as
when they started, the upward force exerted during the trip must average
their total weight, regardless of whether it is exerted constantly (by
holding them), or intermittently (by juggling them). By Newton's law of
action and reaction, this translates into an average downward force that
also equals their weight.
If you can't juggle your way across the
river, is there another weight reduction possibility?
Wrap the balls in your shirt, and drag the package behind you in the
water. As long as the density of the balls doesn't exceed three times
the density of water, the effective weight of three of them in the water
won't exceed the weight of two of them on the raft. (As an alternative,
you could leave the balls on the raft and get in the water yourself -
but watch out for crocodiles).
Rod Schmidt <email@example.com>
reports that wrapping the balls in your shirt and dragging them behind the raft
will work if, and only if, the density of the balls does not exceed three times
the density of the water.
This is because the maximum weight of the three balls in the water must not exceed
the weight of two balls in the raft.
Since the weight of each ball in the water is reduced by the weight of the water
it displaces, the three balls together must displace at least as much water as the
weight of one ball.
In other words, each ball must displace at least one third of its own weight in water.
In order for a ball to displace one third of its weight in water,
its density must not exceed three times the density of the water.
Hey, You Can't Do That!
GE Wagner <firstname.lastname@example.org>
claims that the solutions of dragging the balls along behind are both
incorrect because they removed the balls from the raft (the puzzle
clearly asks "how a person could transport three balls across a river
on a raft") and because their answers wouldn't work with balls
of all compositions.
Removing the person from the raft is a nice idea because the puzzle
doesn't say the raft must support the person. It just says it is capable
of supporting the weight of the person and two balls. However, in a case
where the balls each weighed more than the person, this solution would
still not work.
I do however have a solution for you.
Since all three balls must be on the raft and since the solution must
work no matter the comparative weight of ball to person, the only
solution is to transport an additional item with you that lightens the
Just attach a big helium balloon to the raft. Make sure it's capable of
offsetting the weight of one ball and enjoy your trip.
Editor's note: This solution assumes that there are no overhanging
branches that would snag the balloon or the harness between balloon
http://www.wiskit.com/marilyn/raft.html last updated June 30, 1998 by email@example.com