Volume 34
, Issue 3

1998

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.