Project Euler Problem 20

Project Euler Problem 20

Solution

Answer: 648

We need the sum of the digits of $100!$.

1. Mathematical approach

Compute:

$$100! = 100 \times 99 \times 98 \times \cdots \times 2 \times 1$$

Then convert the resulting integer to digits and sum them.

Python handles arbitrarily large integers, so this is straightforward.

2. Clean Python code

import math

n = math.factorial(100)
digit_sum = sum(int(digit) for digit in str(n))

print(digit_sum)

3. Quick correctness check

We know:

• $10! = 3628800$, whose digit sum is $27$ (matches the example).
• Computing $100!$ exactly and summing its digits gives:

$$648$$

This is the known verified result for Project Euler Problem 20.

Answer: 648