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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.
Screwed-up
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?
Age 11 to 14
Challenge Level
In this question, each of the letters $I$, $R$, $S$ and $T$ represents a different transformation.
We can do one transformation followed by another. For example, $R S$ means ``do $R$, then $S$''.
We can also undo transformations. For example, $R^{-1}$ means ``do the inverse (opposite) of $R$''.
Here are the effects of some transformations on a shape. Can you describe the transformations $I$, $R$, $S$ and $T$?
What single transformation has the same effect as $R S T I R^{-1}S^{-1}T^{-1}I^{-1}$?
This problem is the first of three related problems.
The follow-up problems are Combining Transformations and Simplifying Transformations .
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.