Visualising and representing

problem
Flight of the Flibbins

Age

11 to 14

Challenge level

Blue Flibbins are so jealous of their red partners that they will not leave them on their own with any other bue Flibbin. What is the quickest way of getting the five pairs of Flibbins safely to the new planet?
problem
The root of the problem

Age

14 to 18

Challenge level

Find the sum of this series of surds.
problem
Cubic conundrum

Age

7 to 16

Challenge level

Which of the following cubes can be made from these nets?
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.