Maths and Science Puzzles

This is a random collection of puzzles and brainteasers, some easy, some harder. Why not try them out? Some hints and solutions are on the site, or you can email me. And if you have a favourite puzzle, why not get that added to this page?


Diophantus was a mathematician who lived in Alexandria around AD250. Your task is to deduce his life span from the inscription on his tomb, translated as "He was a boy for the sixth part of his life; grew his beard after a further twelth part; a seventh part followed before he married; five years later he was blessed with a son, but alas the boy perished after attaining only a half of his father's full life span and four years before his father's own death."

Body Parts

Using only words in polite usage!, how many parts of the body can you find with just three letters in their names? There are at least ten.

Hotel Bill

Three friends, each with £10, go to a hotel and book a triple room at £30 for the night. The hotel then realises that it has made a mistake - the room should have cost £25. So the porter is asked to take £5 to the room. He decides to pocket £2 for himself and return £1 to each guest. So each guest has paid £9 and the porter has £2 - making £29. So what has happened to the other £1?

Letter Sequence

What are the next two letters in the following sequence?


Oh my Brother

A beggar has a brother who lives in Spain, but the brother has no brother - can you explain?

Ramanuyan's Number

Ramanuyan was a brilliant, largely self-taught, Indian mathematician. On a trip to London, he boarded a taxi with licence number 1729. Immediately, he pointed out that this was the smallest number that could be formed from the sum of two cubes in two different ways. What are those two ways? (some explanation... 35 is equal to the sum of 3 cubed (ie 27) and 2 cubed (ie 8) ... this is the only possibility for 35)

Looking Backwards

Decode the following phrases - the first has been done for you.

GNIKOOL looking backwards

The Frog

A frog is at the bottom of a 30 metre well. Each day it climbs 5 metres up the side, but it then slips back 3 metres each night. How long does it take to reach the top of the well?

Manhole Cover

Microsoft have used this lateral thinking problem in their job interviews. Can you think of a good reason why a manhole cover is round rather than square?

Five Cheeses

If you like crosswords, this may be for you. What are the following cheeses...

  • Red Chad in revolt
  • Itís made backwards
  • Greek as fate turns out
  • The one after boulder three
  • French author follows mythical beast

Diamond Ring

Alexander and Alexandra live in Afbekistan. It is well known that the postal authorities are corrupt and will open and steal the contents of any package that is not secured with a lock. However, they will leave untouched and safely deliver any package that is locked, even when it is suspected that it may contain valuable items - unless they find the key. Alexander has a diamond ring to send to Alexandra. He has purchased one of the recommended security boxes. These boxes have hasps that can be secured with padlocks. He intends sending the diamond in this box, protected with a padlock, but canít work out how he can send the key securely to Alexandra. They talk on the telephone and devise a solution. What is it?