You can represent ANY positive integer n using only three twos by writing

n= -log₂(log₂(√√...√2))

where log₂ is the logarithm base 2, and there are n square roots.

Can you manage to do the same (that is, represent all positive integers) using three THREEs instead? And by using only TWO twos?

Despite my best efforts, I was unable to derive any other solution apart from the official one.

Nice problem FK.

Posted by K Sengupta on 2007-03-16 10:52:33