Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP
have equal areas. Prove X and Y divide the sides of PQRS in the
Two cubes, each with integral side lengths, have a combined volume equal to the total of the lengths of their edges. How big are the cubes? [If you find a result by 'trial and error' you'll need to prove you have found all possible solutions.]
Is the mean of the squares of two numbers greater than, or less
than, the square of their means?
"On my last birthday, my friend said to me:
'In 15 years' time, your age will be the square of your age 15 years ago!'
Can you work out how old I am?"