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Category Archives: challenges
The birthday candle problem
After a 1.5month 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
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
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
Blockly
It seems that Google is developing a graphical programming language called Blockly, inspired by Scratch but webbased, 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
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 interactive, picture, rectangles, this
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 divisibility, fibonacci
12 Comments
Fun with repunit divisors
In honor of today’s date (11/11/11), here’s a fun little problem (and some followup 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 divisors, primes, repunit
16 Comments