Problems

Blog posts with problems to get your brain going! You get a new problem every fortnight and the solutions are published later.

If you want the problems delivered to your inbox be sure to subscribe to the Problems newsletter.

The next problem is scheduled for Sunday, 24th of January.

You may notice some problems are missing... I'm still migrating articles from my old blog.

Five sailors and their monkey were washed ashore on a desert island. They decide to go get coconuts that they pile up. During the night, each of the sailors, suspicious the others wouldn't behave fairly, went to the pile of coconuts take their fair share. How many coconuts were there in the beginning..?

  585

I bet you have seen one of those Facebook publications where you have a grid and you have to count the number of squares the grid contains, and then you jump to the comment section and virtually no one agrees on what the correct answer should be... Let's settle this once and for all!

  480

Some people are standing quiet in a line, each person with a hat that has one of two colours. How many people can guess their colour correctly?

In this problem you have to devise a strategy to beat the computer in a "guess the polynomial" game.

This simple problem is an example of a very interesting phenomenon: if you have a large enough "universe" to consider, even randomly picked parts exhibit structured properties.

Today we are visiting a specific instance of a well-known basic mathematics game, the 24 Game. The "24 Game" is usually played with younger students because it helps them develop skills related to the basic arithmetic operations.

  567

Take out a piece of paper and a pencil, I am going to ask you to write some letters in your sheet of paper and then I am going to challenge you to fold the sheet of paper... with a twist!

  611

\(n\) mathematicians with numbered party hats gather around in a circle... It is a matter of life or death!

  582

Is it true that every integer you can think of has a multiple written out only with \(0\)s and \(1\)s?

  351

This post's 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!

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!

Gandalf has some Hobbits to appease but his task seems to go on forever. Can you give him a hand..?

Two friends were bored and decided to play a game... a mathematical game with a paper bag!

  594

This post's format will be a bit different from the usual and the first of a series of posts of this type. In this post, I will state a problem and then present my solution.