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# Heptagon Has

A heptagon is a seven-sided polygon. What is the greatest number of the following properties that a single heptagon can possibly possess?

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A heptagon is a seven-sided polygon. What is the greatest number of the following properties that a single heptagon can possibly possess?

- Its interior angles add up to $900$ degrees
- It has exactly four acute interior angles.
- It has no obtuse interior angles.
- All its sides are equal.
- It has exactly one line of symmetry.

This problem is taken from the UKMT Mathematical Challenges.

You can find more short problems, arranged by curriculum topic, in our short problems collection.

This article gives an wonderful insight into students working on the Arclets problem that first appeared in the Sept 2002 edition of the NRICH website.

Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling.