Visualising and representing

problem
Hexagon transformations

Age

7 to 11

Challenge level

Can you cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!
problem
Pyramid numbers

Age

7 to 11

Challenge level

What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?
problem
Fermat's poser

Age

14 to 16

Challenge level

Find the point whose sum of distances from the vertices (corners) of a given triangle is a minimum.
problem
Doesn't add up

Age

14 to 16

Challenge level

In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?
problem
Is there a theorem?

Age

11 to 14

Challenge level

Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?
problem
Tetrahedron faces

Age

7 to 11

Challenge level

One face of a regular tetrahedron is painted blue and each of the remaining faces are painted using one of the colours red, green or yellow. How many different possibilities are there?
problem
Triangle midpoints

Age

14 to 16

Challenge level

You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?
problem
Counting factors

Age

11 to 14

Challenge level

Is there an efficient way to work out how many factors a large number has?
problem
Escriptions

Age

16 to 18

Challenge level

For any right-angled triangle find the radii of the three escribed circles touching the sides of the triangle externally.
problem
Folium of Descartes

Age

16 to 18

Challenge level

Investigate the family of graphs given by the equation x^3+y^3=3axy for different values of the constant a.