A farmer is supplying a mix of seeds, nuts and dried apricots to a manufacturer of crunchy cereal bars. What combination of ingredients costing £5 per kg could he supply?

A decorator can buy pink paint from two manufacturers. What is the least number he would need of each type in order to produce different shades of pink.

Is it always possible to combine two paints made up in the ratios 1:x and 1:y and turn them into paint made up in the ratio a:b ? Can you find an efficent way of doing this?

There are two sets of numbers. The second is the result of the first after an increase by a constant percentage. How can you find that percentage if one set of numbers is in code?

What angle is needed for a ball to do a circuit of the billiard table and then pass through its original position?

Jake sent in a very full solution to the Balancing 3 problem. He identifies a very useful measure to solve this problem.

This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.