data/problems/169.yml
---
:id: 169
:name: Exploring the number of different ways a number can be expressed as a sum of
powers of 2
:url: https://projecteuler.net/problem=169
:content: "Define f(0)=1 and f(<var>n</var>) to be the number of different ways <var>n</var>
can be expressed as a sum of integer powers of 2 using each power no more than twice.\n\nFor
example, f(10)=5 since there are five different ways to express 10:\n\n1 + 1 + 8
\ \n1 + 1 + 4 + 4 \n1 + 1 + 2 + 2 + 4 \n2 + 4 + 4 \n2 + 8\n\nWhat is f(10<sup>25</sup>)?\n\n"