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CS 70
Discrete Mathematics for CS
Spring 2005
Clancy/Wagner
HW 11
Due Thursday, April 21
Coverage:
This assignment involves topics from the lecture of April 14, and from Rosen section 5.3.
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Homework exercises:
1. (10 pts.)
Quadruplyrepeated ones
We say that a string of bits has
k quadruplyrepeated ones
if there are
k
positions where four consec
utive 1’s appear in a row. For example, the string 0100111110 has two quadruplyrepeated ones.
What is the expected number of quadruplyrepeated ones in a random
n
bit string, when
n
≥
3 and all
n
bit strings are equally likely? Justify your answer.
2. (12 pts.)
Stakes well done
Two players, Alice and Bob, each stake 32 pistoles on a threepoint, winnertakeall game of chance.
The game is played in rounds; at each round, one of the two players gains a point and the other gains
none. Normally the first player to reach 3 points would win the 64 pistoles. However, it starts to rain
during the game, and play is suspended at a point where Alice has 2 points and Bob has 1 point. Alice
and Bob have to figure out how to split the money.
You should assume that Alice and Bob are evenly matched, so that in each round Alice and Bob each
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 Fall '08
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