Category Archives: challenges

Fibonacci’s Problem of the Birds

I have been enjoying reading Keith Devlin’s new book, Finding Fibonacci. I’ll write more about the book later. For now, I just wanted to share a nice problem I learned about which Leonardo Pisano, aka Fibonacci, included in his book … Continue reading

Posted in algebra, arithmetic, challenges, people | Tagged , , | 6 Comments

The route puzzle

While poking around some old files I came across this puzzle: (Click for a larger version.) I didn’t make it, and I have no idea where I got it from (do you know?). But in any case, wherever it comes … Continue reading

Posted in arithmetic, challenges, number theory, proof, puzzles | Tagged , , , , , , | 7 Comments

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

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

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

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

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