Sum of 10 natural numbers is 2011, sum of their reciprocals is one. Uses fractions module for exact rational arithmetic, and map-reduce.

new_gist_file.py

#!/usr/bin/env python
from fractions import Fraction

def verify(a):
	return sum(a)== 2011 and sum(map ((lambda n: Fraction(1,n)), a)) == Fraction(1,1)

if __name__=='__main__':
  x = [ [704, 4, 4, 4, 8, 704, 352, 176, 44, 11], [864, 3, 6, 8, 8, 8, 16, 18, 864, 216],
        [912, 3, 4, 4, 19, 24, 912, 57, 38, 38], [920, 10, 5, 10, 23, 23, 920, 92, 4, 4],
        [1080, 4, 4, 6, 9, 12, 12, 20, 432, 432], [1188, 3, 4, 6, 9, 9, 297, 297, 99, 99],
        [1232, 2, 7, 11, 14, 14, 16, 22, 616, 77], [1260, 2, 6, 12, 21, 630, 20, 20, 20, 20],
        [1440, 3, 5, 8, 12, 18, 480, 15, 15, 15], [1500, 6, 10, 10, 10, 10, 12, 375, 75, 3],
        [1560, 3, 6, 10, 10, 10, 10, 12, 312, 78], [1584, 2, 4, 24, 33, 36, 16, 264, 24, 24],
        [1680, 2, 4, 14, 14, 35, 35, 35, 96, 96], [1700, 2, 5, 10, 10, 34, 100, 50, 50, 50],
        [1760, 2, 5, 11, 11, 40, 40, 32, 55, 55], [1800, 2, 6, 12, 18, 20, 20, 40, 18, 75], 
        [1820, 2, 10, 14, 26, 26, 28, 65, 10, 10], [1840, 4, 5, 8, 8, 10, 10, 23, 23, 80],
        [1848, 4, 7, 8, 11, 22, 84, 9, 9, 9], [1872, 3, 8, 8, 8, 13, 13, 16, 18, 52] ]

  print reduce ((lambda x, y: x and y), map( verify, x ))