This is my python solution to the first problem on Project Euler:

n = 1
rn = 0
while n < 1000:
    if n%3 == 0 or n%5 == 0:
        rn += n
    n = n + 1

I would like to find a way to keep everything in this python code to as little number of lines as possible (maybe even a one liner??), and possibly improve the speed (it's currently around 12 ms). By the way, this is the problem:

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.


  • 1
    \$\begingroup\$ sum(n for n in range(1000) if not n%3 or not n%5) \$\endgroup\$
    – dansalmo
    Dec 29 '13 at 21:28
  • \$\begingroup\$ I like your solution to the problem. It is much more efficiently coded than another Project Euler #1 code question I just read. \$\endgroup\$ Apr 4 '16 at 8:50

Python hint number 1:

The pythonic way to do :

n = 1
while n < 1000:
    # something using n
    n = n + 1

is :

for n in range(1,1000):
    # something using n

Python hint number 2:

You could make your code a one-liner by using list comprehension/generators :

print sum(n for n in range(1,1000) if (n%3==0 or n%5==0))

Your code works fine but if instead of 1000, it was a much bigger number, the computation would take much longer. A bit of math would make this more more efficient.

Math hint number 1 :

The sum of all the multiples of 3 or 5 below 1000 is really the sum of (the sum of all the multiples of 3 below 1000) plus (the sum of all the multiples of 5 below 1000) minus the numbers you've counted twice.

Math hint number 2 :

The number you've counted twice are the multiple of 15.

Math hint number 3 :

The sum of the multiple of 3 (or 5 or 15) below 1000 is the sum of an arithmetic progression.

  • \$\begingroup\$ Oh, sorry, my mistake, I inputted 100 instead of 1000 @Josay \$\endgroup\$ Mar 3 '13 at 13:02
  • 2
    \$\begingroup\$ Math hint #4: every number that is divideable by an odd number is an odd number itself (so you can skip half of the loop iterations). @Lewis \$\endgroup\$
    – 11684
    Mar 3 '13 at 17:04

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