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
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
LOGO challenge - triangles-squares-stars

Age

11 to 16

Challenge level

Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.
problem
Hidden rectangles

Age

11 to 14

Challenge level

Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
problem
Königsberg

Age

11 to 14

Challenge level

Can you cross each of the seven bridges that join the north and south of the river to the two islands, once and once only, without retracing your steps?
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
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
All tied up

Age

14 to 16

Challenge level

A ribbon runs around a box so that it makes a complete loop with two parallel pieces of ribbon on the top. How long will the ribbon be?
problem
Inside out

Age

14 to 16

Challenge level

There are 27 small cubes in a 3 x 3 x 3 cube, 54 faces being visible at any one time. Is it possible to reorganise these cubes so that by dipping the large cube into a pot of paint three times you can colour every face of all of the smaller cubes?
problem
Sliced

Age

14 to 16

Challenge level

An irregular tetrahedron has two opposite sides the same length a and the line joining their midpoints is perpendicular to these two edges and is of length b. What is the volume of the tetrahedron?