Number 3 can be expressed as the sum of one or more positive integers in 4 distinct ways:
3; 2 + 1; 1 + 2; 1 + 1 + 1
Number 4 can be expressed as the sum of one or more positive integers in 8 distinct ways:
4; 3 + 1; 1+3; 2 + 2; 2 + 1 + 1; 1+2+1; 1+1+2; 1+1+1+1
Prove : any positive integer n can be so expressed in 2^{n - 1} ways.

(In reply to 3rd solution - elegance by Jer)

I was 100% sure that my hint will trigger this result.

Since it is presented in a perfect way I would like to copy it  as is

when I post the "official solution"

Posted by Ady TZIDON on 2017-03-27 01:21:47