Copyright © University of Cambridge. All rights reserved.

'Weekly Problem 15 - 2012' printed from http://nrich.maths.org/

Show menu


It can possess all five properties.
The description does not say that heptagon has to be convex, i.e. all of its interior angles need not be less than $180^{\circ}$. Since $(2 \timesĀ 7 - 4) \times 90 = 900$, the interior angles of all heptagons total $900^{\circ}$. The creation of a heptagon with all the given conditions is possible as the diagram shows. Notice that four of the interior angles are acute and the other three are reflex angles.

This problem is taken from the UKMT Mathematical Challenges.

View the previous week's solution
View the current weekly problem