Posts Tagged ‘sum’

Problem 22

Friday, March 6th, 2009

Using names.txt, a 46K text file containing over five-thousand first names, begin by sorting it into alphabetical order. Then working out the alphabetical value for each name, multiply this value by its alphabetical position in the list to obtain a name score.

For example, when the list is sorted into alphabetical order, COLIN, which is worth 3 + 15 + 12 + 9 + 14 = 53, is the 938th name in the list. So, COLIN would obtain a score of 938 × 53 = 49714.

What is the total of all the name scores in the file?

I love abusing map.

?View Code PYTHON
import re
 
def word_sum(word):
  word_sum = sum(map(lambda letter: ord(letter)-ord('A')+1, word))
  return word_sum
 
def name_scores_sum(path):
  f = file(path)
  names = f.read()
  names = sorted(re.findall('([A-Z]+)',names))
  sums = map(word_sum,names)
  scores = map(lambda (index,sum): index*sum, enumerate(sums,1))
  return sum(scores)
 
>>> name_scores_sum(path)
871198282

Problem 6

Thursday, January 29th, 2009

The sum of the squares of the first ten natural numbers is,
1^(2) + 2^(2) + … + 10^(2) = 385

The square of the sum of the first ten natural numbers is,
(1 + 2 + … + 10)^(2) = 55^(2) = 3025

Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025 − 385 = 2640.

Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.

?View Code PYTHON
1
sum(range(1,101)) ** 2 - sum( [x**2 for x in range(1,101)] )

Of course there is a simpler way to do this using formulae, but that’s no fun.

Problem 1

Wednesday, January 28th, 2009

If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.

Find the sum of all the multiples of 3 or 5 below 1000.

?View Code PYTHON
1
2
sum (filter (lambda x: x%3 == 0 or x%5 == 0, range (1000)))
233168