# Euler Solution 76

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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