Solving Project Euler Problem 16: Power Digit Sum

The Challenge

Project Euler Problem 16 asks: What is the sum of the digits of the number 2^1000?

This might sound intimidating at first. 2^1000 is an absolutely massive number with over 300 digits! But thanks to Python's built-in support for arbitrarily large integers, this problem becomes surprisingly approachable.

My Solution

Here's the code I used to solve it:

python

n = 2
x = 0
for i in range(1,1000):
    n += n
for i in str(n):
    j = int(i)
    x += j
print(x)

Result: 1366

How It Works

The solution breaks down into two main steps:

Step 1: Calculate 2^1000 Through Repeated Doubling

python

n = 2
for i in range(1,1000):
    n += n

Starting with n = 2, I double it 999 times using n += n. This gives us 2 × 2^999 = 2^1000. It's a clever use of the fact that adding a number to itself is the same as doubling it.

Step 2: Sum the Digits

python

x = 0
for i in str(n):
    j = int(i)
    x += j
print(x)

Once we have our massive 302-digit number, I convert it to a string using str(n). This lets me iterate through each character (digit), convert it back to an integer with int(i), and add it to the running sum.

Why This Approach Works

Python handles big integers seamlessly. Unlike languages like C or Java where you'd hit integer overflow limits, Python automatically handles numbers of any size. This means 2^1000 is just another number to Python, even though it's astronomically large.

String conversion is elegant. Converting a number to a string to access individual digits is a simple, readable approach that works perfectly for this problem.

What I Learned

This problem reinforced a few important concepts:

Python is great for mathematical computing. The ability to work with arbitrarily large integers without any special libraries makes Python ideal for Project Euler problems.

Sometimes simple is best. My repeated doubling approach might not be the most sophisticated, but it's clear, straightforward, and it works.

String manipulation is powerful. Being able to easily convert between numbers and strings opens up simple solutions to what could otherwise be complex problems.

Project Euler continues to be a fantastic way to practice problem-solving and explore different programming techniques. On to the next challenge!