Personal Comment: Something about sticking your hand in a bag and pulling out balls..... Just try simulating this (ewww!) and your answer will come.

Black and White Ball Enigma

What we know: You have a bag with black and white balls in it. You close your eyes, take out of the bag a random pair of balls, open your eyes, look at them and put them away. If both were of the SAME COLOR you put in the bag ONE BLACK BALL, else put in the bag A WHITE BALL (assume that you have an equal number of black and white balls).

Enigma: Will this proccess ever empty the box? How many balls will there be available for the "last" step: One ball? Two balls? If you KNOW the exact number of the balls in the box, can you know before the procedure, THE COLOR OF THE LAST BALL IN THE BOX?

Solution: The white balls either do not decrease at all, or decrease in pairs. SO if the original number of the white balls was ODD, the last ball must be WHITE. If the number of the white balls was EVEN, the last ball must be BLACK. DISCUSSION: The process will eventualy empty the box (its too probable to discuss). The last ball depends on the number of the white balls. Not the exact number. All we need is if its odd or even. Nothing else.
From the following URL:
www.eexi.gr/phase2

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