Category Archives: challenges

The chocolate bar game: losing positions characterized

Posted on January 20, 2016 by Brent

The evident pattern from my last post is that losing positions in the chocolate bar game appear to be characterized by those where the binary expansion of is the same as the binary expansion of with any number (including zero) … Continue reading →

Posted in challenges, games, pattern, pictures | Tagged , , , , , , , , | 1 Comment

The chocolate bar game: losing positions in binary

Posted on January 18, 2016 by Brent

Recall the chocolate bar game from my last post, whose winning and losing positions can be visualized like this: Here’s a list of some losing positions on or above the main diagonal (dark blue squares in the above picture), ordered … Continue reading →

Posted in challenges, games, pattern, pictures | Tagged , , , , , , , , | 1 Comment

The birthday candle problem

Posted on August 7, 2015 by Brent

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 , , , | 5 Comments

Straightedge and compass construction challenges

Posted on June 29, 2013 by Brent

I haven’t written here in quite a while—I’ve switched into “work on research for my dissertation really hard so that I can actually graduate” mode, and with a 21-month old in the mix that leaves very little time for blogging. … Continue reading →

Posted in challenges, games, geometry, links, meta | Tagged , , , , , , | 5 Comments

Making connections

Posted on April 20, 2013 by Brent

Here’s something fun I was playing around with today. I generated 100 random points and connected some of them with lines. Can you figure out how I chose which lines to draw? How about these? (Same points, different lines.) Or … Continue reading →

Posted in challenges, geometry | Tagged , , , | 10 Comments

Permuting permutations

Posted on December 18, 2012 by Brent

As you probably know, there are ( factorial) different ways to put the numbers from through (or any set of distinct objects) in a list. For example, here are the different lists containing the numbers through : Each such list … Continue reading →

Posted in challenges, combinatorics | Tagged , | 11 Comments

Blockly

Posted on June 28, 2012 by Brent

It seems that Google is developing a graphical programming language called Blockly, inspired by Scratch but web-based, with the ability to compile down to JavaScript, Dart, or Python (or raw XML, so you can process it further). I can’t say … Continue reading →

Posted in challenges, programming | Tagged , , , , | 7 Comments

Picture this

Posted on June 13, 2012 by Brent

Picture this! is a very cool interactive thingy, made by Jason Davies, intended to get students (or anyone, really) thinking about some interesting math. Go play around with it and see if you can answer any of the listed questions … Continue reading →

Posted in challenges, links, pattern, pictures | Tagged , , , | 6 Comments

Fibonacci multiples

Posted on May 15, 2012 by Brent

I haven’t written anything here in a while, but hope to write more regularly now that the semester is over—I have a series on combinatorial proofs to finish up, some books to review, and a few other things planned. But … Continue reading →

Posted in arithmetic, challenges, fibonacci, number theory, pattern | Tagged , | 12 Comments

Fun with repunit divisors

Posted on November 11, 2011 by Brent

In honor of today’s date (11/11/11), here’s a fun little problem (and some follow-up problems) I’ve seen posed in a few places (for example, here is a very similar problem). If I recall correctly, it was also a problem on … Continue reading →

Posted in arithmetic, challenges, modular arithmetic, number theory, primes | Tagged , , | 16 Comments