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

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

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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?

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Which dilutions can you make using only 10ml pipettes?

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

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

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

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

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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. . . .

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Is there a temperature at which Celsius and Fahrenheit readings are the same?

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

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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. . . .

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

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

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

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

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

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

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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?

An article for teachers which discusses the differences between ratio and proportion, and invites readers to contribute their own thoughts.

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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.

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

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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.

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The Pythagoreans noticed that nice simple ratios of string length made nice sounds together.

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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. . . .

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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?

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

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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?

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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. . . .

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At the beginning of the night three poker players; Alan, Bernie and Craig had money in the ratios 7 : 6 : 5. At the end of the night the ratio was 6 : 5 : 4. One of them won $1 200. What were the. . . .

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A cyclist and a runner start off simultaneously around a race track each going at a constant speed. The cyclist goes all the way around and then catches up with the runner. He then instantly turns. . . .

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

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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?

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Two motorboats travelling up and down a lake at constant speeds leave opposite ends A and B at the same instant, passing each other, for the first time 600 metres from A, and on their return, 400. . . .

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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?

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In a race the odds are: 2 to 1 against the rhinoceros winning and 3 to 2 against the hippopotamus winning. What are the odds against the elephant winning if the race is fair?

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In the ancient city of Atlantis a solid rectangular object called a Zin was built in honour of the goddess Tina. Your task is to determine on which day of the week the obelisk was completed.

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

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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.

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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.

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

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

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

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

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

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If the sides of the triangle in the diagram are 3, 4 and 5, what is the area of the shaded square?

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