### Meta

### Categories

- algebra (47)
- arithmetic (86)
- books (35)
- calculus (7)
- challenges (58)
- combinatorics (29)
- complex numbers (6)
- computation (83)
- convergence (9)
- counting (38)
- famous numbers (48)
- fibonacci (18)
- fractals (13)
- games (34)
- geometry (72)
- golden ratio (8)
- group theory (28)
- humor (8)
- induction (8)
- infinity (19)
- iteration (24)
- links (76)
- logic (12)
- meta (43)
- modular arithmetic (30)
- number theory (108)
- open problems (11)
- paradox (1)
- pascal's triangle (8)
- pattern (106)
- people (23)
- pictures (74)
- posts without words (42)
- primes (57)
- probability (9)
- programming (20)
- proof (93)
- puzzles (18)
- recursion (16)
- review (25)
- sequences (28)
- solutions (31)
- teaching (16)
- trig (3)
- Uncategorized (6)
- video (19)

### Archives

- June 2021 (1)
- May 2021 (1)
- March 2020 (4)
- February 2020 (1)
- January 2020 (7)
- December 2019 (4)
- November 2019 (2)
- October 2019 (5)
- September 2019 (7)
- August 2019 (3)
- July 2019 (5)
- May 2019 (4)
- April 2019 (2)
- March 2019 (3)
- February 2019 (3)
- January 2019 (4)
- November 2018 (3)
- October 2018 (4)
- September 2018 (4)
- August 2018 (6)
- July 2018 (2)
- June 2018 (5)
- May 2018 (3)
- April 2018 (5)
- March 2018 (4)
- February 2018 (3)
- January 2018 (4)
- December 2017 (3)
- November 2017 (3)
- October 2017 (1)
- September 2017 (1)
- July 2017 (4)
- June 2017 (4)
- May 2017 (9)
- April 2017 (7)
- March 2017 (5)
- February 2017 (4)
- January 2017 (3)
- December 2016 (4)
- November 2016 (6)
- October 2016 (6)
- September 2016 (2)
- August 2016 (5)
- July 2016 (2)
- June 2016 (4)
- May 2016 (4)
- April 2016 (2)
- March 2016 (3)
- February 2016 (9)
- January 2016 (8)
- December 2015 (5)
- November 2015 (29)
- August 2015 (3)
- June 2015 (2)
- April 2015 (1)
- May 2014 (1)
- December 2013 (1)
- October 2013 (1)
- July 2013 (1)
- June 2013 (1)
- May 2013 (1)
- April 2013 (3)
- March 2013 (3)
- February 2013 (2)
- January 2013 (5)
- December 2012 (3)
- November 2012 (4)
- October 2012 (5)
- September 2012 (1)
- August 2012 (4)
- July 2012 (1)
- June 2012 (6)
- May 2012 (2)
- April 2012 (3)
- March 2012 (1)
- February 2012 (4)
- January 2012 (5)
- December 2011 (1)
- November 2011 (7)
- October 2011 (4)
- September 2011 (6)
- July 2011 (2)
- June 2011 (4)
- May 2011 (5)
- April 2011 (2)
- March 2011 (4)
- February 2011 (1)
- January 2011 (1)
- December 2010 (1)
- November 2010 (4)
- October 2010 (2)
- September 2010 (1)
- August 2010 (1)
- July 2010 (1)
- June 2010 (2)
- May 2010 (3)
- April 2010 (1)
- February 2010 (6)
- January 2010 (3)
- December 2009 (8)
- November 2009 (7)
- October 2009 (3)
- September 2009 (3)
- August 2009 (1)
- June 2009 (4)
- May 2009 (5)
- April 2009 (4)
- March 2009 (2)
- February 2009 (1)
- January 2009 (7)
- December 2008 (1)
- October 2008 (2)
- September 2008 (7)
- August 2008 (1)
- July 2008 (1)
- June 2008 (1)
- April 2008 (5)
- February 2008 (4)
- January 2008 (4)
- December 2007 (3)
- November 2007 (12)
- October 2007 (2)
- September 2007 (4)
- August 2007 (3)
- July 2007 (1)
- June 2007 (3)
- May 2007 (1)
- April 2007 (4)
- March 2007 (3)
- February 2007 (7)
- January 2007 (1)
- December 2006 (2)
- October 2006 (2)
- September 2006 (6)
- July 2006 (4)
- June 2006 (2)
- May 2006 (6)
- April 2006 (3)
- March 2006 (6)

# Category Archives: probability

## Have a piece of PIE

Commenter Stuart LoPresti gave a very nice analysis answering the questions at the end of my last post. And indeed, the punchline is that the answers are very similar to the answers to the post before that. PIE If we … Continue reading

## Probabilistic PIE

Commenters Sylvain B., xpil, and Christian Luca all gave correct answers to the challenge from my previous post. If the probability that someone likes X is , then the probability they don’t like X is . Therefore the probability that … Continue reading

## A probabilty puzzle

Suppose that we have surveyed a certain population of people, and have determined the following probabilities: The probability that a person likes anchovies is . The probability that a person likes to read books is . The probability that a … Continue reading

## 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