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What is the color of the last marble left in the bag?

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A bag contains 80 blue marbles and 70 red marbles. Next to this bag is a pile of blue and red marbles. We take the marbles out of the bag in groups of two, with the following rules:

If the two marbles are of the same color, we put them in the pile and place a blue marble back into the bag.
If the two marbles are of different colors, we put them in the pile and place a red marble back into the bag.

What is the color of the last marble left in the bag?

posted Oct 15, 2018 by anonymous

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1 Answer

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The last marble is blue.
.
The red marbles are removed in pairs.
Either via Red/Red => 2 red marbles removed
Or via Red/Blue => 0 red marbles removed (1 removed + 1 gained).
.
Thus the last marble cannot be red.

answer Oct 15, 2018 by Jcm



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