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During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?

Challenge Level

Can you rank these quantities in order? You may need to find out extra information or perform some experiments to justify your rankings.

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Nirmala and Riki live 9 kilometres away from the nearest market. They both want to arrive at the market at exactly noon. What time should each of them start riding their bikes?

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In this version of the story of the hare and the tortoise, the race is 10 kilometres long. Can you work out how long the hare sleeps for using the information given?

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Alice's mum needs to go to each child's house just once and then back home again. How many different routes are there? Use the information to find out how long each road is on the route she took.

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Use the interactivity to move Pat. Can you reproduce the graphs and tell their story?

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

Challenge Level

Two trains set off at the same time from each end of a single straight railway line. A very fast bee starts off in front of the first train and flies continuously back and forth between the. . . .

Challenge Level

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its speed at each stage.

Challenge Level

Two engines, at opposite ends of a single track railway line, set off towards one another just as a fly, sitting on the front of one of the engines, sets off flying along the railway line...

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N people visit their friends staying N kilometres along the coast. Some walk along the cliff path at N km an hour, the rest go by car. How long is the road?

A paradox is a statement that seems to be both untrue and true at the same time. This article looks at a few examples and challenges you to investigate them for yourself.

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A train leaves on time. After it has gone 8 miles (at 33mph) the driver looks at his watch and sees that the hour hand is exactly over the minute hand. When did the train leave the station?

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How far have these students walked by the time the teacher's car reaches them after their bus broke down?

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A security camera, taking pictures each half a second, films a cyclist going by. In the film, the cyclist appears to go forward while the wheels appear to go backwards. Why?

Challenge Level

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its vertical and horizontal movement at each stage.

Challenge Level

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects the distance it travels at each stage.

Challenge Level

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