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'''Problem 1.''' Bob is rolling a <math>6</math>-sided die. Every time he rolls a number that he has already rolled before, he rolls again. He stops when he has rolled all the numbers. What is the expected number of rolls it will take Bob? | '''Problem 1.''' Bob is rolling a <math>6</math>-sided die. Every time he rolls a number that he has already rolled before, he rolls again. He stops when he has rolled all the numbers. What is the expected number of rolls it will take Bob? | ||
Revision as of 15:07, 21 May 2013
Questions
Problem 1. Bob is rolling a 
-sided die. Every time he rolls a number that he has already rolled before, he rolls again. He stops when he has rolled all the numbers. What is the expected number of rolls it will take Bob?
Problem 2. Suppose you have a rectangular box, with side lengths 
and 
, where 
. We launch a point-like ball from one of the vertices with an angular degree of 
. The ball bounces off the sides of the box. Pretend there is no friction, drag, or anything else to slow down the ball. Prove or disprove that the ball won't ever hit a vertex again.
Problem 3. In a country, there is a particular way the cities inside are connected. One city has only one road leading out of it. One city has two roads leading out of it. Two cities have three roads leading out of it. Three cities have 5 roads leading out of it. In general, 
cities have 
roads leading out of it. What values of 
are there such that this setup is possible?
