# Euler Solution 76

### From ProgSoc Wiki

t is possible to write five as a sum in exactly six different ways:

4 + 1 3 + 2 3 + 1 + 1 2 + 2 + 1 2 + 1 + 1 + 1 1 + 1 + 1 + 1 + 1

How many different ways can one hundred be written as a sum of at least two positive integers?

# Solutions

## Python by Althalus

Runtime: 373 seconds (slow and steady wins the race?)

""" I cheated a little. I might do that more often. Psyco acts kind of like a Just In Time compiler, drastically improving run times.... (copy and paste down to and including psyco.full() to use the psyco module in your own python apps...) """ import sys sys.path.append('/home/progsoc-users/althalus/python/') import psyco from psyco.classes import * psyco.full() #This is a slight rewrite of my solution to problem 31. hence the random references to coins. coins = range(1,101) def recurse(total,n): count = 0 total -= n if total == 0: return 1 elif total < 0: return 0 elif total > 0: for i in coins[:n]: count += recurse(total,i) return count return total total = 0 for i in range(1,101): total+= recurse(100,i) print i,total print total