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National Endowment for Humanities Olympics Athens 13-29 August 2004 Caifornia Department of Education American Association of Physics Teachers JPL National Science Teachers Association

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Olympics USA 2004

........................... INTERESTING TEST QUESTIONS

1. Name a body part that almost everyone on earth has an above average number of! Justify your answer.

2. A woman and her husband attended a party with four other couples. As is normal at parties, handshaking took place. Of course, no one shook their own hand or the hand of the person they came with.

...And not everyone shook everyone else's hand. But when the woman asked the other (9) people present how many different people's hands they had shaken they all gave a different answer. Question (this is NOT a trick!): How many different people's hands did the woman's husband shake?

3. A man starts walking up a narrow mountain path at 6:00 a.m. He walks at different speeds, stopping to eat, sometimes going back a few steps to look at a flower, but never leaving the path. He eventually arrives at the top at 10:00 p.m. the same day. He camps out over night and starts down the same path at 6:00 a.m. the next day. After stopping to eat and so forth he arrives at the bottom at 10:00 p.m.

True or false? There is some point on the path that the man occupied at exactly the same time on the two different days. Explain your answer.



1. Fingers. Most people have all their fingers (10). Of the remaining people, it is far more common to have fewer than 10 fingers than to have more than ten fingers. Thus the average number of fingers is nine point something. Thus, almost all people have an above average number of fingers.

2. The maximum number of hands that any person might have shaken is eight. Therefore, the nine people asked by the woman must have given the answers 0, 1, 2, 3, 4, 5, 6, 7, 8. Let's refer to the person who answered 1 as person 1. Person 8 must have shaken everybody's hand but their own and their spouse's. Thus, everyone except their spouse has shaken at least one hand. Therefore, 8 and 0 are married. Similarly, 7 must have shaken everybody's hand except for 0 and 1 (who used up his/her shake with 8). So 1 must be 7's spouse (0 is spoken for). Continuing in this way we see that (6 and 2) and (5 and 3) are married to each other. This leaves 4 as the only unmatched person. 4 must therefore be matched to the woman.

3. Imagine that on the first day a clone of the man starts down the mountain at 6:00 a.m. and arrives at the bottom by 10:00 p.m.The man and the clone have to pass each other at some point.


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