Working systematically

Which of these games would you play to give yourself the best possible chance of winning a prize?

Here are two games you can play. Which offers the better chance of winning?

How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?

A visualisation problem in which you search for vectors which sum to zero from a jumble of arrows. Will your eyes be quicker than algebra?

When I park my car in Mathstown, there are two car parks to choose from. Can you help me to decide which one to use?

Can you find the hidden factors which multiply together to produce each quadratic expression?

Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?

Is it possible to find the angles in this rather special isosceles triangle?

What is the largest number which, when divided into these five numbers in turn, leaves the same remainder each time?

Can you find a general rule for finding the areas of equilateral triangles drawn on an isometric grid?