Volume 48
, Issue 3

2012

As we go to press there has been a lot of excitement in mathematics about the proof of the ABC conjecture.
This column's topic will be a theorem in the mathematical theory of games.
This article is about a family of polynomials introduced by James H.
Problem 1
The infinite nested radical $$c=\sqrt{1+2\sqrt{1+2\sqrt{1+2\sqrt{1+2\sqrt{\ldots}}}}}$$ converges.
 
Find $c$. 
 
Solution 1
 
Note that if \( c=\sqrt{1+2\sqrt{1+2\sqrt{1+2\sqr
Competition Winners – Senior Division
First Prize
John Papantoniou                                    Sydney Gr
Q1401 Solve the recurrence relation
$$a(n)=6a(n-1)-9a(n-2)\ ,\quad a(0)=2\ ,\quad a(1)=21\ .$$
Q1391 Jack looked at the clock next to his front door as he left home one afternoon to visit Jill and watch a TV programme.  Arriving exactly as the programme started, he set out for home again when it finished one hour later.