Category Archives: challenges

Post without words #5

Posted in challenges, pattern, pictures, posts without words | 4 Comments

The chocolate bar game: losing positions characterized

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

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The chocolate bar game: losing positions in binary

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

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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 , , , | 5 Comments

Straightedge and compass construction challenges

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

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

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