Solution to Purple Turtles

Let g be the number of green turtles and p be the number of purple turtles.

If four of the purple turtles turned green, I would have g+4 green turtles and p−4 purple turtles. If then half the green turtles turned purple, I would have (g+4)/2 = g/2+2 green turtles and p−4+([g+4]/2) = p+g/2−2 purple turtles.

By the same token, if four of the green turtles turned purple and then half the purple turtles turned green, I would have p/2+2 purple turtles and g+p/2−2 green turtles.

According to the statement of the puzzle, I would have twice as many purple turtles the first way as the second way. That is,

p + g/2 − 2=2(p/2 + 2)
p + g/2 − 2=p + 4

So I have 12 green turtles and an unknown number of purple turtles!

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