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

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

Can you prove that there are arbitrarily many primes in arbitrarily big intervals?

Three mathematicians discuss a beautiful flower garden and the coloured flowers within.

Two realtors discuss who's netting the award for highest average commission, but it isn't clear who the winner is...

Please help me identify these 100 light bulbs by turning ON and OFF their switches.

Can you find the centre of the circle with just five lines?

How many matches does it take to find the winner of a tennis tournament?

Can you make the pyramid point the other way by moving only three coins?

Can you help these kids trick or treat their entire neighbourhood in this Halloween special?

If I scramble a Rubik's cube for long enough, will it solve itself?

It's night time and 4 friends need to cross a fragile bridge, but they only have one torch. What's the order in which they should cross?

Three friends are given three different numbers that add up to a dozen. Can you figure out everyone's numbers?

You have two magical ropes that you can set on fire and you need to count 45 minutes. How do you do it?

You are on vacation and must find the most efficient way to cross all bridges. How will you do that?

Alice and Bob sit across each other, ready for their game of coins. Who will emerge victorious?

This is an algorithmic puzzle where you just have to turn some coins.

Two doors, one gives you eternal happiness and the other eternal sadness. How can you pick the correct one?

Syncro is a beautiful game where you have to unite all the petals in a single flower. In how many moves can you do it?

A waiter at a restaurant gets a group's order completely wrong. Can you turn the table to get two or more orders right?

A bunch of ants are left inside a very, very, tight tube, and they keep colliding with each other and turning around. How long will it take them to escape?

You are sunbathing when you decide to go and talk to some friends under a nearby sun umbrella, but first you want to get your feet wet in the water. What is the most efficient way to do this?

This problem is a step up from Problem #028 - hidden key. Can you tackle this one?

There is a key hidden in one of three boxes and each box has a coin on top of it. Can you use the coins to let your friend know where the key is hiding?

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..?

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!

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.

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!

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

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.

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!

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.