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24 July, 07:09

Your spaceship crash-lands on Neptune. On Neptune, there are three different species of beast, each of which, remarkably, resembles a delicious, wholesome dessert back here on Earth. Our scientists have accordingly named them the blancmange, the halo-halo, and the mousse. In a particular colony, scientists observed 36 blancmanges, 37 halo-halos, and 38 mousses. These extraterrestrial confections have a curious property: when any two individuals of different species touch, they both spontaneously transform into the third type. (So for example, a halo-halo and a mousse would become two blancmanges.) Is it possible that all the creatures eventually become the same species? (Hint: there is an invariant modulo

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  1. 24 July, 09:48
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    it is impossible for all creatures to become the same species.

    Explanation:

    According the exercise:

    blancmange=36

    halo-halo=37

    mouses=38

    if one blancmange and one halo-halo have contact with each other, I will have:

    blancmange=36-1=35

    halo-halo=37-1=36

    mouses=38+2=40

    if you want to keep the population of mice on the rise, this proportion must continue, therefore:

    blancmange=36-36=0

    halo-halo=37-36=1

    mouses=38+36+36=110

    The maximum amount of mouses is 110. According to these data, it is impossible for all creatures to become the same species.
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