# Siam's fighting fish

The inhabitants of Siam are born players who would bet their clothes on any bet that offered a chance of winning or losing. They are not belligerent but love to witness a fight among other creatures, from toads to elephants. Dog fights or cockfights are a daily occurrence and are carried out following the common trends of civilized countries ... but nowhere else on earth is it possible to see a fight between fish!

They have two kinds of fish that despite being good food are raised and valued exclusively for their qualities as fighters. One of them is a large white perch known as king fish and the other is a small black carp or devil fish. Between these two species there is such a rivalry that they are attacked just by seeing each other and the battle is life or death.

A king fish can defeat one or two of the little devil fish in a few seconds but the devil fish are so agile and work together so tightly that three of them can match one of the big ones so they can fight for hours Without any result.

Its line of attack is so precise and studied that four of the devil fish can kill a large one in three minutes and a larger number of devil fish kill their opponent in a proportional time. That is, five devil fish can kill a king fish in two minutes and 24 seconds, six in two minutes, etc.

This combination of adverse forces is so precise and invariable that when a tournament is held you can always calculate the exact time it will take for a certain number of fish of a species of a species to defeat a specific number of its enemies.

The illustration shows four king fish fighting thirteen devil fish.

Who will win? And how long will it take one species to annihilate the other?

To avoid ambiguities in the statement proposed by Loyd, we must clarify that devil fish always attack a king fish in groups of three or more and that they remain with it until they finish it.

#### Solution

The devil fish will be the winners of the contest and the way to calculate the time it will take to kill the king fish is as follows:

Three little fishes matched forces with each of the three big fishes entertaining them while the other four little fighters liquidated the fourth king fish in 3 exact minutes.

Then, five little ones took care of a big one and killed him in 2 minutes and 24 seconds, while the other little fish kept the rest of the big ones at bay.

It is clear that if the remaining two groups had been helped with one more fighter, they would all have finished at the same time, since each of the large fish has only resistance to demand the energy of a small fish for 2 minutes and 24 seconds. Therefore, if the attackers are now seven instead of one, they will do so in 1/7 of that time, or 20 seconds and 4/7.

By dividing the forces of the fish to attack the two remaining large fish, one will be attacked by seven and the other by six, at the end of the 20 seconds and 4/7 the last king fish would still need the punishment that a fish can administer in that span.

The thirteen little ones, concentrating their attack, will end the big fish in 1/13 of that time or 1 second and 53/91.

Adding the total time of the various rounds we have 3 minutes, 2 minutes and 24 seconds, 20 seconds and 4/7, and 1 second and 53/91, so the total time that the battle lasted is 5 minutes 46 seconds and 2/13 of a second.