Can you cover all of the rational numbers in [0, 1] with tiny intervals?
Split the numbers 0, 1, ..., 15 into two sets with sum interesting properties!
In high school I had a colleague that had his birthday on the same day as I did. What a coincidence, right? Right..?
Given some paper squares, can you slice them and then glue them back together to form a single square?
Is it true that every integer you can think of has a multiple written out only with \(0\)s and \(1\)s?
I find the problem in this post rather fun to think about because it is a problem about a game that can actually be played between two players.
In this post we will talk about three different, all very common, ways of writing proofs: proofs by construction, by contrapositive and by contradiction.
This problem is a really interesting problem I solved two times. The first time I solved it I failed to prove exactly how it works... then some years later I remembered the problem statement and was able to solve it properly. Let's see how you do!
I have always loved solving mazes... so naturally I had to write a program to solve mazes for me!
In this post I talked about the riddle of the water buckets. Now I challenge you to prove that in some situations it is impossible to solve it!
Can you measure exactly \(2\)L of water with two plain buckets with volumes of \(14\)L and \(5\)L? Of course you can!
A regular expression, without much rigor, is a very compact way of representing several different strings. Given a regular expression (regex), can I find out all the strings the regex can find?
Let's prove that there are two irrational numbers, call them \(a\) and \(b\), such that \(a^b\) is a rational number! And let's do it in a tweet.
Gandalf has some Hobbits to appease but his task seems to go on forever. Can you give him a hand..?
