Long ago, there existed a species of fighting
chameleons. These chameleons were divided into six types of
matching color and strength:
Black were the strongest, followed by
blue,
green,
orange,
yellow and
white which were the weakest.
Whenever two chameleons of the same color met, they would fight to the
death and the victor would become stronger and change color (eg white to yellow). Black chameleons would fight eternally.
The small island of Ula was initially populated by a
group of fighting chameleons. For this group
a) the colors present each had an equal number of
chameleons (for example, group = 3 black, 3 green and 3 yellow)
b) it was not made up entirely of white chameleons
After all the possible fighting was done, there remained one black and
green and no blue or orange chameleons.
How many white chameleons remained in the island?
Prove it.
Okay - I'm obviously missing something in this puzzle as I have come up with two starting populations that result in different numbers of resulting Whites (I'm assuming that weaker chameleons are never victors in combat over their stronger cousins):
4 Greens and 4 Whites:
Combat 1: (Green vs Green) = 1 Blue, 2 Greens, 4 Whites
Combat 2: (Blue vs Green) = 1 Black, 1 Green, 4 Whites
(1 black, 1 green, no blues or oranges - meets condition)
2 Greens and 2 Whites:
Combat 1: (Green vs White) = 1 Blue, 1 Green, 1 White
Combat 2: (Blue vs White) = 1 Black, 1 Green
(1 black, 1 green, no blues or oranges - meets condition)
So, in one we end up with all the whites surviving, in the other they're all dead.
My main problem here is that there seems to be no necessity for any chameleon to actually have met any other. As a result, whites can avoid combat (and potential death) by being hermit-chameleons...
Is there something that is supposed to be implied in the question that negates one or both of these above options?
What am I missing?
