Suppose the following lottery is conducted a large number of times. There are n people (you can assume n is fairly large or you could let it be 100 or 1000 if you like) and each writes a positive integer on a piece of paper. The winner is the one who writes the smallest unique positive integer. For example, if 4 people write a 1 and 2 people write a 2 and only one person writes a 3, ther person who wrote a 3 is the winner.
So my question is, if this game is played a large number of times, which is the average of all the winning numbers.
In case you were curious, I have been prefacing some of my recent math questions with "Math Challenge:" in order to (a) signify that this is not my homework and (b) possibly add a bit of excitement =) However, unlike the previous ones, I have no idea what the answer to this is, or if there even is one, but I would be very interested in people's thoughts.
By the way, I once played this game with about 30 people and the number 2 won!
2007-10-06
14:30:59
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3 answers
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asked by
Phineas Bogg
6
in
Mathematics