# Problems

## Logic puzzles, riddles, & maths problems

##### Problem #065 β clock synchronisation

When will these two clocks synchronise again?

##### Problem #064 β infinite mathematicians with hats

How can an infinite number of mathematicians figure out their own hat colours?

##### Problem #063 β arbitrarily many primes in arbitrarily big intervals

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

##### Problem #062 β sliding coins

Can you align all of the coins on the right edge of the board?

##### Problem #061 β flower garden

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

##### Problem #060 β realtor commissions

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

##### Problem #059 β marching pegs

How can you swap the coloured pegs if they can only march forward?

##### Problem #057 β how to find the circle centre

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

##### Problem #056 β tennis tournament

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

##### Problem #055 β horse racing

25 horses racing, and you have to find out the fastest ones!

##### Problem #054 β imperfect compression

Can you show that perfect compression is impossible?

##### Problem #053 β weighing the odd one out

Can you find the fake ball by weighing it?

##### Problem #052 β chessboard domino

Can you tile a chessboard with two missing squares?

##### Problem #051 β queens and knights

How many queens and knights can you place on a chessboard?

##### Problem #050 β 8 queens

In how many ways can you place 8 queens on a chessboard?

##### Problem #049 β coin pyramid

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

##### Problem #048 β trick or treat

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

##### Problem #046 β triangle grid

Can you draw 4 triangles in this 5 by 5 grid, covering all dots?

##### Problem #045 β 1, 2, 3

Figure out the number I'm thinking of with a single question!