Pythagoras' theorem

problem
Cubestick

Age

16 to 18

Challenge level

Stick some cubes together to make a cuboid. Find two of the angles by as many different methods as you can devise.
problem
Golden construction

Age

16 to 18

Challenge level

Draw a square and an arc of a circle and construct the Golden rectangle. Find the value of the Golden Ratio.
problem
Where to land

Age

14 to 16

Challenge level

Chris is enjoying a swim but needs to get back for lunch. How far along the bank should she land?
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
Folded over

Age

14 to 16

Challenge level

A rectangular piece of paper is folded. Can you work out one of the lengths in the diagram?
problem
Out of the window

Age

14 to 16

Challenge level

Find out how many pieces of hardboard of differing sizes can fit through a rectangular window.
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
The spider and the fly

Age

14 to 16

Challenge level

A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?
problem
Far horizon

Age

14 to 16

Challenge level

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?