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APPLES AND ORANGES
You have three boxes, one containing apples, one
containing oranges, and one containing apples and
oranges. Each box is labelled, one as "apples," one
as "oranges," and the last as "apples and oranges."
The trouble is that all three boxes are labelled
incorrectly! You are allowed to reach into one and
only one box, and pull one and only one fruit out of
it. Whatever the fruit is, you should now be able to
label all the boxes correctly! How?
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Answer
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PAIRS OF SOCKS
Mr. MacGillicuddy owns exactly 24 pairs of socks, 12
pairs white and 12 pairs black. He never sorts them
after doing the laundry, figuring it's so easy to
just get a pair in the morning, as white and black
are easy to tell apart. One night he gets an
emergency phone call and has to rush to get dressed
and out of the house. On the way to his dresser, the
lights go out, and he is left in pitch-black
darkness. He wants to look reasonably normally
dressed, but cannot see the socks to tell them apart! Being resourceful, he comes up with a solution. He
will pull the smallest number of socks from the
drawer, get dressed except for socks, and put on a
matching pair of socks when he gets into his car and
turns on the internal car light. What is the smallest number of socks he can pull out and still guarantee
himself of having one matching pair of socks?
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THE A-FRAME HOUSE
Mr. Macgillicuddy's father lives in an A-frame house. The roof forms a fairly sharp angle at the top. One day MacGillicuddy, Sr. went outside and, while looking around at the fair weather, noticed that his favorite rooster was sitting right at the peak of his roof. MacGillicuddy, Sr. began to wonder what would happen if the rooster laid an egg and wrote his son to pose the problem. Given that the earth rotates west to east and MacGillicuddy, Sr.'s house is oriented exactly north to south, and the egg landed squarely at the peak of the roof's angle, which direction would the egg roll toward? His son, ever resourceful, shot back his answer immediately. What was it?
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