Hello again!

Here's another riddle, which I hope will be met better than the previous one.

There's a planet inhabited by arbuzoids (water-melon-ers). Those creatures are found in three colors: red, green and blue. There are 13 red arbuzoids, 15 blue ones, and 17 green. When two differently coloured arbuzoids meet, they both change to the third color.

The question is, can it ever happen that all of them assume same color?

Anton

Here's another riddle, which I hope will be met better than the previous one.

There's a planet inhabited by arbuzoids (water-melon-ers). Those creatures are found in three colors: red, green and blue. There are 13 red arbuzoids, 15 blue ones, and 17 green. When two differently coloured arbuzoids meet, they both change to the third color.

The question is, can it ever happen that all of them assume same color?

Anton

Comments

I wouldn't exactly call this a "riddle"!

The answer is no.

I was intrigued by the word "arbuzoid", by the way. I'm guessing this derives from the Russian word for watermelon. Is that right?

Mr WordyYou're right about both the word's origin (arbuz == water melon) and the answer to the riddle. But let me ask you why do you think it technically does not qualify as a riddle, and what your solution is. Some people that I have asked it tended to answer "no" after a thought experiment wherein they tried every way to have them all take the same color and failed. But that doesn't prove there's no solution...

Ant_222SPOILER FOLLOWS.

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This is how I did it. Assign the number 0 to the red arbuzoid, 1 to the blue, and 2 to the green. The sum of all the arbuzoids taken modulo 3 is invariant under the allowed transformations. With 13 red arbuzoids, 15 blue and 17 green, the sum, modulo 3, is 1. However, if all 45 arbuzoids were of the same colour, it would be 0. Therefore it's impossible to get from one to the other just by performing the allowed transformations.

Mr WordyAnt_222Mr WordyAnt_222