I found this quotation in WordPress and it just took me:
If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.
John von Neumann
Very true, indeed!
Very Interesting Problem
I just heard of a very interesting problem from my colleague. I would like to think about it some time, but since I have absolutely no time now, I propose it for you, my dear reader.
Let’s assume we have an integer n and an alphabet consisting of five symbols – `1`, `+`, `*`, `(`, and `)`. What is the biggest integer we can write down using no more than n symbols from our alphabet?
For example, if n=3, the biggest integer will be 2 (that is, 1+1); if n=15, my guess – it will be 9 ((1+1+1)*(1+1+1)), etc.
What is seen at once – there is only a sense of looking to just odd integers n because all the legal expressions can be only of an odd length.
So, what can we think about the answer – is it possible to make a function f(n) giving the right integer value depending only on n? Or maybe it is just possible to make a function with some other arguments as well? Maybe it isn’t possible at all to make such a function, but just to make an algorithm constructing such an integer? What do you think about it anyway?
