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# Category Archives: probability

## Network reliability

Over on my other blog I’ve started writing about an interesting but apparently nontrivial problem, which some readers of this blog may find interesting as well. Suppose you have a network of computers with some one-directional wires between them. Each … Continue reading

## The birthday candle problem: solution

Recall the birthday candle problem I wrote about in a previous post: A birthday cake has lit candles. At each step you pick a number uniformly at random and blow out candles. If any candles remain lit, the process repeats … Continue reading

Posted in combinatorics, probability, solutions
Tagged birthday, candles, expectation, problem
5 Comments

## The birthday candle problem

After a 1.5-month epic journey1, I am finally settling into my new position at Hendrix College. Here’s a fun problem I just heard from my new colleage Mark Goadrich: A birthday cake has lit candles. At each step you pick … Continue reading

Posted in challenges, combinatorics, probability
Tagged birthday, candles, expectation, problem
5 Comments

## The mathematics of human knots

Have you ever played “human knot”? It seems to be a common icebreaker/team-building sort of exercise (just do a Google search for “human knot” and you’ll find quite a few pages discussing it). Everyone stands in a circle, then reaches … Continue reading

Posted in games, people, probability
Tagged games, human, icebreaker, knot, team, teambuilding
9 Comments

## Change probabilities

Hello, dear reader! If you are a new reader, welcome! (I know there is at least one of you—thanks to commenter sg211 for prompting me to post again. =) I must apologize for dropping the ball on writing up the … Continue reading

Posted in challenges, counting, probability
17 Comments

## Challenge #7

This delightful problem is courtesy of Diana Davis (don’t follow the link unless you want to see the solution, though!), although I did take the liberty of formulating it slightly differently. =) One bright and sunny day, you’re walking down … Continue reading

Posted in challenges, geometry, probability
7 Comments