Question: A well-known problem concerns a mythical country that has three cities, A, B and C, with a total population of 2400. At the end of

A well-known problem concerns a mythical country that has three cities, A, B and C, with a total population of 2400. At the end of each year it is decreed that all people must move to another city, half to one and half to the other. If a, b and c are the populations in the cities A, B and C respectively, show that in the next year the populations are given by

b' || -|-| 2 D

Supposing that the three cities have initial populations of 600, 800 and 1000, what are the populations after ten years and after a very long time (a package such as MATLAB is ideal for the calculations)?

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