Volume 34


In our paper we showed how to fold a regular $7$-gon - and much else besides!  We showed which convex polygons could be folded by a period-$2$ folding procedure these turned out to be those polygons whose number of sides,  $s$, had the form $$s=\frac{2^{m+n}-1}{2^n-1} $$

One of the most famous problems in the history of dynamics is the brachistochrone problem.

SENIOR DIVISION,  Equal first prize of $200 and a certificate: VARODAYAN David, Sydney Grammar School;  ELLIOT Justin Koonin,     Sydney Grammar School

Q.1035 Find all positive integers $n$ and $m$ such that $n$ is a factor of $4m − 1$ and $m$ is a factor of $4n − 1$.

Q. 1016 Show how six cylindrical pencils of equal radius each with neither end sharpened can be put into mutual contact along their curved surfaces.