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2001 Spatial Oddity

With one cut a piece of card 16 cm by 9 cm can be made into two pieces which can be rearranged to form a square 12 cm by 12 cm. Explain how this can be done.


A cylindrical helix is just a spiral on a cylinder, like an ordinary spring or the thread on a bolt. If I turn a left-handed helix over (top to bottom) does it become a right handed helix?

Counting Triangles

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

Making Rectangles, Making Squares

Age 11 to 14
Challenge Level

Imagine you have any number of equilateral triangles all of the same size as well as a large number of $30$ $^\circ$ , $30$ $^\circ$ , $120$ $^\circ$ isosceles triangles with the shorter sides the same length as the equilateral triangles.

Using these triangles how many differently shaped rectangles can you build?

Can you make a square?

Printable NRICH Roadshow resource.