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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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