Project Euler Problem 16 Solution: Power digit sum

Project Euler Problem 16 Statement

2¹⁵ = 32768 and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26.

What is the digit sum for the number 2¹⁰⁰⁰ ?

Solution

Using arbitrary–precision integer arithmetic

print (sum(map(int, str(pow(2, 1000)))))

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Python natively supports arbitrary–precision integers and arithmetic using as many digits as there is available memory to perform a calculation. We use that feature to our full advantage to provide a simple solution to this problem.

To solve this problem, we calculate 2¹⁰⁰⁰ (302 digits long) and convert the result to a string so we can iterate over each character–digit (integers are not iterable, but strings are).

Then, using the map function, we iterate over the string and convert every character–digit back to an integer using the int function. Finally, we calculate a digit sum by adding them together using the sum function.

HackerRank version

Solves all test cases for Hackerrank Project Euler Problem 16

HackerRank Project Euler 16 requires a little more scale by having you to solve up to 100 test cases with a higher limit for 2ⁿ, where n ≤ 10,000.

Python Source Code

n = int(input("2's exponent? "))
print ("Sum of the digits of 2 ^", n, " = ", sum(map(int, str(pow(2, n)))))

Run Project Euler Problem 16 using Python on repl.it.

Last Word

Using native language arbitrary–precision structures.

Simply embrace the power of arbitrary–precision integers and ignore the call to solve it in some primitive way. It’s evolution – get used to it.