# Problems

## Logic puzzles, riddles, & maths problems

##### Problem #024 - hats in a line

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?

##### Problem #023 - guess the polynomial

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

##### Problem #022 - coprimes in the crowd

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.

##### Problem #020 - make 24 with 3 3 8 8

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.

##### Problem #019 - fold the alphabet

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!

##### Problem #018 - circle of hats

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

##### Problem #017 β shuffle me around

There's 100 drawers and 100 shuffled balls. Can you find the one I choose?

##### Problem #016 β hamburger dilemma

I mixed up my hamburgers while cooking. Can you help me out?

##### Problem #015 β cover me not

Can you cover all of the rational numbers in [0, 1] with tiny intervals?

##### Problem #014 β the sum of the parts

Split the numbers 0, 1, ..., 15 into two sets with sum interesting properties!

##### Problem #013 β circular train

Can you find out how many carriages this circular train has?

##### Problem #011 β salvation of the monks

How can 2018 monks find eternal peace?

##### Problem #012 β it is just a matter of time

How often do the hands of a clock overlap?

##### Problem #010 β Alice and the Maths Hatter

How can 4 friends guess their own hat colours?

##### Problem #009 β greedy pirates

How can a greedy pirate captain keep his treasure to himself?

##### Problem #008 β cutting squares

Given some paper squares, can you slice them and then glue them back together to form a single square?

##### Problem #007 - binary multiples

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

##### Problem #006 - stacks of beans

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.

##### Problem #005 - number me right

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!

##### Problem #004 - solvability of the water buckets

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!