Difference between revisions of "User talk:Bobthesmartypants"
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==Bobthesmartypants's question collection== | ==Bobthesmartypants's question collection== | ||
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? | 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? | ||
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| + | 2. Suppose you have a rectangular box, with side lengths <math>a</math> and <math>b</math>, where <math>a,b\in\mathbb{Z}</math>. We launch a point-like ball from one of the vertices with an angular degree of <math>60^{\circ}</math>. 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. | ||
Revision as of 11:15, 21 May 2013
Bobthesmartypants's question collection
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?
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.
