Logic puzzles, riddles, & maths problems

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When will these two clocks synchronise again?

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

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

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

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...

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

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?

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

Can you show that perfect compression is impossible?

Can you find the fake ball by weighing it?

Can you tile a chessboard with two missing squares?

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

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

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?

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

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