Looking for mathematical mind-benders ? Why not mull over these mystifying morsels .
Food for thought
The Ham Sandwich Theorem helps to show us how the universe behaves … with the aid of a savoury snack . Take two slices of bread , a slice of cheese and a slice of ham and make the messiest-looking sandwich ever . The bread on top is not exactly lined up , the cheese slice is a very odd shape . Half the ham is hanging out on one side . Now cut it EXACTLY in half . The theorem says that there is a plane ( in this example , a knife ) that could slice through the bread , ham and cheese in one cut to create two perfectly equal-sized sandwich halves . There is also one plane that would equally divide all the objects in half even when one slice of bread has plopped onto the floor , the other is still on the plate , the cheese is in your hand and the ham has somehow ended up stuck to the ceiling ( picture it as a laser beam and imagine what the angle would have to be , slicing through space ). The mystery is WHERE you make the cut !
Small but perfectly formed
When A . A . Milne wrote a poem about how excellent it is to be 6 years old , he may or may not have known that 6 is the smallest perfect number .* A perfect number is a number that can only be divided by the numbers that add up to make it ( except for the number itself , of course ). Six can be divided by 1 , 2 and 3 . Now add all those ‘ divisors ’ together 1 + 2 + 3 and you get … 6 . Can you work out the divisors that add up to make the next perfect number , 28 ? Erm , yeah sure . Just gimme a sec … Ed
There are around 30 known perfect numbers . Out of an infinity of numbers , that doesn ’ t sound like many , right ? The only trouble is , the next biggest number after 28 is 496 , and the next one after that is 8,128 ….
* Not to be confused with Pythagoras ’ perfect number , which is 10 .
6