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.
(In reply to
re: change wording.. by levik)
This is also where I got confused too. I assumed that it couldn't be 'all possible' fights as the only end result from any starting set would be X black chameleons - everything else would be killed off and the black would be fighting, but wouldn't kill each other off. No single green one, and zero whites (obviously), would be involved in the end state. This is why I assumed it wasn't 'all possible' and was just some transitionary state between the given start conditions and final result (and, as a result, was why I ended up at my initially stated confusion). I'm not certain now what the condition of the question's "final state" actually are...
Sorry for this, Cheradenine - I can't see what's being asked here, though... Ick - sorry! :-/
re(2): change wording..
