Project Euler 22, off by 18,609

Change this line:

names = sorted(str(string).split(","))

to:

names = sorted(string[0].split(','))

File contains just one line, so you need to access that line using string[0]. file.readlines returns a list containing all lines from the file, it's better to do something like:

names = f.read().split(',')
names.sort()

A shorter version of your program:

from string import ascii_uppercase
def score(word):
    return sum(ascii_uppercase.index(c) + 1 for c in word.strip('"'))

with open('names.txt') as f:
  names = f.read().split(',')
  names.sort()
print sum(i*score(x) for i, x in enumerate(names, 1))

_{Note: string is a built-in module, don't use it as a variable name}