At one point, a remote island's population of chameleons was divided as follows:

• 13 Red chameleons
• 15 Green chameleons
• 17 Blue chameleons

Each time two different colored chameleons would meet, they would change their color to the third one. (I.E. If Green meets Red, they both change their color to Blue.)

Is it ever possible for all chameleons to become the same color? (Why or why not?)

its not possible (i think) cause if the reds met greens, they'd turn blue and there would be 2 extras. those two would meet the 17 blues and youd have 13 blues, 2 reds, 15 more blues and then if the reds met blues, there would be 28 blues and 2 greens. if the greens met blues, there would be 26 blues and 2 reds, and then if any met any it would repeat all over again!

here is another way to work it out-

if::::
15 greens
meet 17 blues
there'd be 15 reds
and 2 blues.
(there is still 13 reds, and then those 15 reds, but there is 2 blues).

if 2 blues
met 28 reds,
youd have 4 greens
and 26 reds
blues, youd have 0.
then if 4 greens
met 26 reds,
youd have 8 blues
and 22 reds
then if the
8 blues
met the 22 reds
youd have 16 greens
and 15 reds.
THEN
if the 15 reds
spotted the 16 greens
youd have
30 blues
and 1 green
if 1 green met
30 blues
there would be 2 reds
and 29 blues
and as long as they keep meeting, they will keep changing, adding double the lesser amount to the color that both or them arent

therefore, it isn't possible for the chameleons to all be the same color

Posted by sariz on 2002-04-20 14:32:52