Can you explain why every year must contain at least one Friday the thirteenth?

Christmas trees are planted in a rectangular array of 10 rows and 12 columns. The farmer chooses the shortest tree in each of the columns... the tallest tree from each of the rows ... Which is the taller tree, A or B?

Sometime during every hour the minute hand lies directly above the hour hand. At what time between 4 and 5 o'clock does this happen?

A ladder 3m long rests against a wall with one end a short distance from its base. Between the wall and the base of a ladder is a garden storage box 1m tall and 1m high. What is the maximum distance up the wall which the ladder can reach?

Chris is enjoying a swim but needs to get back for lunch. If she can swim at 3 m/s and run at 7m/sec, how far along the bank should she land in order to get back as quickly as possible?

What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?

Have you ever wondered what it would be like to race against Usain Bolt?

Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?

Can you work out which processes are represented by the graphs?

A collection of short Stage 3 and 4 problems on Mathematical Modelling.