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 |

g/2 | = | 6 |

g | = | 12 |

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

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Col. George Sicherman [ HOME | MAIL ]