The sums of the squares of three related numbers is also a perfect square - can you explain why?
Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?
A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?
Can you find the area of a parallelogram defined by two vectors?
The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?
Manufacturers need to minimise the amount of material used to make their product. What is the best cross-section for a gutter?
How many intersections do you expect from four straight lines ? Which three lines enclose a triangle with negative co-ordinates for every point ?
Your school has been left a million pounds in the will of an ex-pupil. What model of investment and spending would you use in order to ensure the best return on the money?
Charlie has moved between countries and the average income of both has increased. How can this be so?
Two boats travel up and down a lake. Can you picture where they will cross if you know how fast each boat is travelling?
