Visualising and representing

problem
Triangles and petals

Age

14 to 16

Challenge level

An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?
problem
Clocked

Age

11 to 14

Challenge level

Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?
problem
John's train is on time

Age

11 to 14

Challenge level

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?
problem
The Deca Tree

Age

7 to 11

Challenge level

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.
problem
Trebling

Age

7 to 11

Challenge level

Can you replace the letters with numbers? Is there only one solution in each case?
problem
Eggs in baskets

Age

5 to 7

Challenge level

There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. How many eggs are in each basket?
problem
Hello again

Age

11 to 14

Challenge level

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?
problem
Convex polygons

Age

11 to 14

Challenge level

Show that among the interior angles of a convex polygon there cannot be more than three acute angles.
problem
Corridors

Age

14 to 16

Challenge level

A 10x10x10 cube is made from 27 2x2 cubes with corridors between them. Find the shortest route from one corner to the opposite corner.
problem
Counters

Age

7 to 11

Challenge level

Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?