A problem from a highschool maths book.....

ive been trying to work this one out for years.

 

Mr and Mrs Wombat live in a house in which the floor of every room is a square and covered with identical square tiles. Mrs Wombat's room contains 101 tiles more than Mr Wombat's room. How many tiles does Mrs Wombat's room contain?

You've been trying for years? Since the rooms are square the tiles are even multiples, like 4x4, 5x5, 6x6, etc. There's probably a formula but you can just keep multiplying numbers by themselves to find the answer. Or find a multiplication table that goes up that high.

 

Her multiple is only one higher than his multiple, if that helps you with a starting point.

Let small room be n*n and large (n+m)*(n+m)

 

ie (n+m)^2 -n^2 = 101

or m*(2n+m) = 101

 

ie m is a factor of 101, which is prime

therefore m = 1, n =50