Urning It
An urn contains 50 balls, each of which is either red or blue.
We know the following two facts.
I) At least one ball in the urn is red.
II) If you take any two balls out at random from the urn, at least one of them will be blue.
How many blue balls are in the urn?
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1 solution
If there were as many as two red balls in the urn, you could randomly select those two and invalidate statement II. Therefore, at most one ball in the urn can be red. But by statement I, at least one ball in the urn is red. Therefore, EXACTLY one ball in the urn is red. So the number of blue balls is 50 - 1 = 49.