The triathlon is a physically gruelling challenge. Can you work out which athlete burnt the most calories?

Two perpendicular lines lie across each other and the end points are joined to form a quadrilateral. Eight ratios are defined, three are given but five need to be found.

Anne completes a circuit around a circular track in 40 seconds. Brenda runs in the opposite direction and meets Anne every 15 seconds. How long does it take Brenda to run around the track?

Using an understanding that 1:2 and 2:3 were good ratios, start with a length and keep reducing it to 2/3 of itself. Each time that took the length under 1/2 they doubled it to get back within range.

Mike and Monisha meet at the race track, which is 400m round. Just to make a point, Mike runs anticlockwise whilst Monisha runs clockwise. Where will they meet on their way around and will they ever. . . .

Two buses leave at the same time from two towns Shipton and Veston on the same long road, travelling towards each other. At each mile along the road are milestones. The buses' speeds are constant. . . .

The Earth is further from the Sun than Venus, but how much further? Twice as far? Ten times?

If it takes four men one day to build a wall, how long does it take 60,000 men to build a similar wall?

A garrison of 600 men has just enough bread ... but, with the news that the enemy was planning an attack... How many ounces of bread a day must each man in the garrison be allowed, to hold out 45. . . .

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

Is it cheaper to cook a meal from scratch or to buy a ready meal? What difference does the number of people you're cooking for make?

When Charlie retires, he's looking forward to the quiet life, whereas Alison wants a busy and exciting retirement. Can you advise them on where they should go?

Move the point P to see how P' moves. Then use your insights to calculate a missing length.

How long will it take Mary and Nigel to wash an elephant if they work together?

Which dilutions can you make using only 10ml pipettes?

Which is a better fit, a square peg in a round hole or a round peg in a square hole?

Build a scaffold out of drinking-straws to support a cup of water

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. . . .

My recipe is for 12 cakes - how do I change it if I want to make a different number of cakes?

Can you find an efficent way to mix paints in any ratio?

Can you work out how to produce different shades of pink paint?

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?

Which dilutions can you make using 10ml pipettes and 100ml measuring cylinders?

The large rectangle is divided into a series of smaller quadrilaterals and triangles. Can you untangle what fractional part is represented by each of the ten numbered shapes?

What's the most efficient proportion for a 1 litre tin of paint?

Read all about the number pi and the mathematicians who have tried to find out its value as accurately as possible.

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

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

Some of the numbers have fallen off Becky's number line. Can you figure out what they were?

Scientists often require solutions which are diluted to a particular concentration. In this problem, you can explore the mathematics of simple dilutions

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

Can you fill in the mixed up numbers in this dilution calculation?

Which exact dilution ratios can you make using only 2 dilutions?

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?

The diagram shows a regular pentagon with sides of unit length. Find all the angles in the diagram. Prove that the quadrilateral shown in red is a rhombus.

Construct a line parallel to one side of a triangle so that the triangle is divided into two equal areas.

Imagine you were given the chance to win some money... and imagine you had nothing to lose...

A right circular cone is filled with liquid to a depth of half its vertical height. The cone is inverted. How high up the vertical height of the cone will the liquid rise?

Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP have equal areas. Prove X and Y divide the sides of PQRS in the golden ratio.

Andy is desperate to reach John o'Groats first. Can you devise a winning race plan?

Four jewellers share their stock. Can you work out the relative values of their gems?

The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?

One night two candles were lit. Can you work out how long each candle was originally?

Straight lines are drawn from each corner of a square to the mid points of the opposite sides. Express the area of the octagon that is formed at the centre as a fraction of the area of the square.