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Subj:.....The Fighting Fishes Of Siam (S631)
          From the book 
            "Mathematical Puzzles of Sam Loyd" 
          Edited by Martin Gardner 
          From: Dover Publications in 1959

How long will it take one species
of fish to vanquish the other?

The people of Siam are natural born gamblers who would bet
their last vestige of clothing upon any event which offers
a chance to win or lose.  They are not especially belli-
gerent themselves, but they love to witness a fight between
any other creatures from toads to elephants.  Dog-fights,
or cocking mains are of daily occurence and are conducted
pretty much according to the recognized lines of civilized
countries, but in no other land upon the globe is it possible
to witness a fish fight!

They have two kinds of fish which, despite their being very
choice food, are raised and valued solely for their fighting
qualities.  The one is a large white perch known as the king
fish, and the other is the little black carp or devil fish.
Such antipathy exists between these two species that they
attack each other on sight and battle to the death.

A king fish could readily dispose of one or two of the little
fish in just a few seconds, but the devil fish are so agile
and work together so harmoniously that three of the little
fellows would just equal one of the big ones, and they would
battle for hours without any results.  So cleverly and
scientifically do they carry on their line of attack that
four of the little fellows would kill a large one in just
three minutes and five would administer the coup de grace
proportionately quicker.  (E.g., five would kill one king
fish in two minutes and 24 seconds, six in two minutes,
and so on.)

These combinations of adverse forces are so accurate and
reliable that when a fish tournament is arranged, one can
calculate the exact time it will take a given number of one
kind to vanquish a certain number of the enemy.

By way of illustration a problem is presented in wiich four
of the king fish oppose thirteen of the little fighters.
Who should win?  And how long should it take one side to
annihilate the other?

[To avoid an ambiguity in Loyd's statement of the problem,
it should be made clear that the devil fish always attack
single king fish in groups of three or more, and stay
with the large fish until he is disposed of.  We cannot,
for example, assume that while the twelve little fish hold
the four large fish at bay, the thirteenth devil fish darts
back and forth to finish off the large fish by attacking
all of them simultaneously.  If we permit fractions, so to
speak, of devil fish to be effective then we can reason that
if four devils kill a king in three minutes, thirteen devils
will finish a king in 12/13 minutes, or four kings in 48/13
minutes (3 minutes, 41 and 7/13 seconds).  But this same
line of reasoning would lead to conclude that twelve devils
would kill one king in one minute, or four kings in four
minutes, even without the aid of the thirteenth little fish
- a conclusion that clearly violates Loyd's assumption that
three little fish are unable to kill one devil fish. - M.G.]


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