Being resilient

Can you make sense of information about trees in order to maximise the profits of a forestry company?

Chris and Jo put two red and four blue ribbons in a box. They each pick a ribbon from the box without looking. Jo wins if the two ribbons are the same colour. Is the game fair?

The area of a square inscribed in a circle with a unit radius is 2. What is the area of these other regular polygons inscribed in a circle with a unit radius?

The sums of the squares of three related numbers is also a perfect square - can you explain why?

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?

Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice?

Can you work out the fraction of the original triangle that is covered by the inner triangle?

Can you find the area of a parallelogram defined by two vectors?

Various solids are lowered into a beaker of water. How does the water level rise in each case?

Two boats travel up and down a lake. Can you picture where they will cross if you know how fast each boat is travelling?