Sum of all the multiples of 3 or 5 below 1000

Question

Beginner here- trying to make a simple python program that will compute/answer this 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. Currently this is what I have: ``` a = 0 b = 0 while a < 1000: a = a + 3 print (a) while b < 1000 b = b + 5 print (b) ``` This will print all the numbers being considered. I just need to add them together and that's my answer. I would like one of two things to happen, instead of the code that I have written: - I would like all of this to happen internally, and therefore not have to use the "print" function. The just print the sum of all of those multiples. - I would like all of this stuff to print, but then I want to be able to print the sum of all of them too. Is there a way to make the computer take the value of everything it has printed?

Accepted Answer

Actually this problem can be solved in O(1) instead of O(N) without using any loops or lists:

The required sum is the sum of all multiples of 3 plus sum of all multiples of 5 minus the sum of multiples of (3*5=15) below the given number 1000 (LIMIT=999). The sums are calculated as a sum of arithmetic series. It can be calculated in following way:

```
LIMIT=999

# Get the upper bounds for the arithmetic series
upper_for_three = LIMIT // 3
upper_for_five = LIMIT // 5
upper_for_fifteen = LIMIT // 15

# calculate sums
sum_three = 3*upper_for_three*(1 + upper_for_three) / 2
sum_five = 5*upper_for_five*(1 + upper_for_five) / 2
sum_fifteen = 15*upper_for_fifteen*(1 + upper_for_fifteen) / 2

# calculate total
total = sum_three + sum_five - sum_fifteen

# print result with Python 3
print(int(total))
```

The result is:

```
>>> 
233168
```

Sum of all the multiples of 3 or 5 below 1000

Solution

Problem