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