Question 320497
<pre><b>
Suppose there are N club members.

We can choose the president as any of the N club members and the 
Vice-President any of the remaining N-1 club members, so:

{{{N*(N-1)}}}{{{"="}}}{{{72}}}

{{{N^2-N}}}{{{"="}}}{{{72}}}

{{{N^2-N-72}}}{{{"="}}}{{{0}}}

{{{(N-9)(N+8)}}}{{{"="}}}{{{0}}}

{{{matrix(2,3,

N-9=0, "|", N+8=0,
N=9, "|", N=-8)}}}

Disregard the negative solution.

There are 9 club members.

Edwin</pre>