The Best of Creative Computing Volume 1 (published 1976)

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AEDI, MUTAB, NEDA, and SOGAL (puzzle to determine probability of winning war)

```Problems for Creative Computing....

AEDI, MUTAB, NEDA and SOGAL

by Walter Koetke

Lexington High School

Your non-terrestrial thoughts should not remain free of problems that require
creative solutions. Toward that end, here are two situations that you might find
interesting. After solving either one or both of these problems, please send
your solution to Walter Koetke at the Creative Computing address. The best
solutions received will be acknowledged in a future column.

If you think you've seen the first problem before, you may be correct. It's
really an old problem in a new disguise.

The civilizations of the three planets Neda, Mutab and Sogal have agreed to
begin a war in the year 2431. Although these societies have not eliminated such
irrational actions as war, they have at least formalized the process. There are,
for instance, no guerilla activities and wars are usually very brief and always
decisive. Wars are fought with inter-planetary rockets each of which is powerful
enough to completely destroy an entire planet. With such powerful weapons at
their disposal, Neda, Mutab and Sogal have agreed to the following set of rules,
for only in this way can they be assured of a single victor.

Rule 1: The fight will continue until only one civilization remains.

Rule 2: The rather primitive technique of drawing lots will be used to determine
which planet may launch the first rocket, which the second and which the third.

Rule 3: After the launching rotation is established, rocket launching begins and
continues in order until only one planet remains.

When contemplating the outcome of this war, the three civilizations have full
knowledge of the background of their adversaries.

Mutab is clearly the technologically superior civilization. Once launched, their
rockets always strike with perfect accuracy - thus disproving a modern theory
that nothing is perfect. Before this war begins, both of the other civilizations
are aware of the terrifying fact that if a Mutab rocket is fired at them, the
probability of their being completely destroyed is 1.

Neda is the oldest civilization and long ago had the superior technology.
However, the complacency of a self-centered, unchallenged mind has been eroding
this superiority for many years. As a result, the technology of Neda has not
advanced in over 40 years. If a Nedian rocket is fired at another planet, the
probability of hitting that planet is 0.8, just as it was 40 years ago.

Sogal is by far the newest of the three civilizations. Being dedicated to
producing its own technology on its own terms has resulted in a proud and
purposeful civilization, but one that is technologically four to five hundred
years behind its present adversaries. A missile launched by Sogal has only a
50-50 chance of reaching its intended target.

Your role in this future war is to determine each civilization's probability of
winning.

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