Solving Project Euler Problem 13: Large Sum

Project Euler Problem 13 asks us to find the first ten digits of the sum of one hundred 50-digit numbers. It's a straightforward problem that mainly tests how well you can handle large numbers in your chosen programming language.

The Problem

We have 100 numbers, each with exactly 50 digits:

37107287533902102798797998220837590246510135740250
46376937677490009712648124896970078050417018260538
74324986199524741059474233309513058123726617309629
...

Add them all up and return the first 10 digits of the result.

Handling Large Numbers

The main issue is that these numbers are too big for standard integer types in most languages. You'd need big integer libraries in languages like C++ or Java, but Python handles arbitrary precision integers natively, which makes this problem much simpler.

My Solution

The approach is straightforward:

1. Split the input string into individual numbers

2. Convert each to an integer

3. Sum them all

4. Extract the first 10 digits

python

# Split into individual numbers
y = x.split('\n')

# Convert to integers and sum
y = list(map(int, y))
z = sum(y)

# Get first 10 digits
a = list(str(z))
j = []

for index, i in enumerate(a):
    if index <= 9:
        j.append(i)

k = ''.join(j)

Results

• Sum: 5537376230390876637302048746832985971773659831892672 (52 digits)

• First 10 digits: 5537376230

Notes

This problem shows why Python is convenient for mathematical problems - what could require complex big integer implementations in other languages just works out of the box. The solution is direct and readable.

You could optimize this further (since we only need 10 digits, we don't technically need the full sum), but for Project Euler's purposes, the straightforward approach works fine and is easy to understand.