Visualising and representing

problem
Efficient cutting

Age

11 to 14

Challenge level

Use a single sheet of A4 paper and make a cylinder having the greatest possible volume. The cylinder must be closed off by a circle at each end.
problem
Fred the class robot

Age

7 to 11

Challenge level

Billy's class had a robot called Fred who could draw with chalk held underneath him. What shapes did the pupils make Fred draw?
problem
Classic cube

Age

16 to 18

Challenge level

The net of a cube is to be cut from a sheet of card 100 cm square. What is the maximum volume cube that can be made from a single piece of card?
problem
Slippage

Age

14 to 16

Challenge level

A ladder 3m long rests against a wall with one end a short distance from its base. Between the wall and the base of a ladder is a garden storage box 1m tall and 1m high. What is the maximum distance up the wall which the ladder can reach?
problem
3D treasure hunt

Age

14 to 18

Challenge level

Some treasure has been hidden in a three-dimensional grid! Can you work out a strategy to find it as efficiently as possible?
problem
Something in common

Age

14 to 16

Challenge level

A square of area 3 square units cannot be drawn on a 2D grid so that each of its vertices have integer coordinates, but can it be drawn on a 3D grid? Investigate squares that can be drawn.
problem
Integral polygons

Age

11 to 14

Challenge level

Each interior angle of a particular polygon is an obtuse angle which is a whole number of degrees. What is the greatest number of sides the polygon could have?
problem
Hexagon cut out

Age

11 to 14

Challenge level

Weekly Problem 52 - 2012
An irregular hexagon can be made by cutting the corners off an equilateral triangle. How can an identical hexagon be made by cutting the corners off a different equilateral triangle?
problem
Circuit training

Age

14 to 16

Challenge level

Mike and Monisha meet at the race track, which is 400m round. Just to make a point, Mike runs anticlockwise whilst Monisha runs clockwise. Where will they meet on their way around and will they ever meet at the start again? If so, after how many circuits?
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?