Visualising and representing

problem
LOGO challenge - circles as animals

Age

11 to 16

Challenge level

See if you can anticipate successive 'generations' of the two animals shown here.
problem
Frogs

Age

11 to 14

Challenge level

How many moves does it take to swap over some red and blue frogs? Do you have a method?
problem
Think of two numbers

Age

11 to 14

Challenge level

Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
problem
Cubist cuts

Age

11 to 14

Challenge level

A 3x3x3 cube may be reduced to unit cubes in six saw cuts. If after every cut you can rearrange the pieces before cutting straight through, can you do it in fewer?
problem
Triangles to tetrahedra

Age

11 to 14

Challenge level

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
problem
Three cubed

Age

7 to 11

Challenge level

Can you make a 3x3 cube with these shapes made from small cubes?
problem
Two primes make one square

Age

7 to 11

Challenge level

Can you make square numbers by adding two prime numbers together?
problem
Coloured edges

Age

11 to 14

Challenge level

The whole set of tiles is used to make a square. This has a green and blue border. There are no green or blue tiles anywhere in the square except on this border. How many tiles are there in the set?
problem
Reach 100

Age

7 to 11

Challenge level

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
problem
Trace the edges

Age

7 to 11

Challenge level

On which of these shapes can you trace a path along all of its edges, without going over any edge twice?