Question

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

Answer 1

Answer:

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.