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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.

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?

Triangular Tantaliser

Draw all the possible distinct triangles on a 4 x 4 dotty grid. Convince me that you have all possible triangles.


Age 11 to 14 Challenge Level:

A cylindrical helix is just a spiral on a cylinder, like an ordinary spring or the thread on a bolt. There are two kinds, a right-handed helix and a left-handed helix and in the case of a bolt one has to be turned clockwise to screw it down and the other anti-clockwise. If I turn a left-handed helix over (top to bottom) does it become a right handed helix? Give as simple an explanation as you can.