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, 15th of November.

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

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.

Alice and Bob are going to be locked away separately and their faith depends on their guessing random coin tosses!

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.

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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!

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

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

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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.

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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!

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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.