Visualising and representing

problem
Icosian game

Age

11 to 14

Challenge level

This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.
problem
Playground snapshot

Age

7 to 14

Challenge level

The image in this problem is part of a piece of equipment found in the playground of a school. How would you describe it to someone over the phone?
problem
Marbles in a box

Age

11 to 16

Challenge level

How many winning lines can you make in a three-dimensional version of noughts and crosses?
problem
Cutting a cube

Age

11 to 14

Challenge level

A half-cube is cut into two pieces by a plane through the long diagonal and at right angles to it. Can you draw a net of these pieces? Are they identical?
problem
Overlap

Age

14 to 16

Challenge level

A red square and a blue square overlap. Is the area of the overlap always the same?
problem
A tilted square

Age

14 to 16

Challenge level

The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
problem
Triangular tantaliser

Age

11 to 14

Challenge level

Draw all the possible distinct triangles on a 4 x 4 dotty grid. Convince me that you have all possible triangles.
problem
Tilting triangles

Age

14 to 16

Challenge level

A right-angled isosceles triangle is rotated about the centre point of a square. What can you say about the area of the part of the square covered by the triangle as it rotates?
problem
Prime magic

Age

7 to 16

Challenge level

Place the numbers 1, 2, 3,..., 9 one on each square of a 3 by 3 grid so that all the rows and columns add up to a prime number. How many different solutions can you find?
problem
Counting triangles

Age

11 to 14

Challenge level

Triangles are formed by joining the vertices of a skeletal cube. How many different types of triangle are there? How many triangles altogether?