Category Archives: challenges

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

Blockly

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

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

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

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