Problem 16 Project Euler Solution with Python

Power digit sum

2¹⁵ = 32768 and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26.
What is the sum of the digits of the number 2¹⁰⁰⁰?

Again a very simple and direct problem, if you were to solve it using python. I am not going to explain any algorithm because, in this program we have just used inbuilt python functions and have got the result.

Program

The program is as follows:

File: pep16.py -------------- #http://radiusofcircle.blogspot.com #time module for calculating execution time import time #Time at the start of execution start = time.time() #converting each and every digit to list a = list(str(2**1000)) #converting every element in a list from #str to int a = [int(x) for x in a] #Power Digit Sum pds = sum(a) #Printing the output print 'Power digit sum of 2**1000 is: '+str(pds) #time at the end of execution end = time.time() #printing the time of execution print end-start

All the code is well commented and I am assuming that you can understand it.
If you want to download this program you can download it from Github Gist.

Output

Summary

This problem was pretty easy to solve. This problem just involved brushing up of our concepts in the python programming language.

The code is well commented and so I have not explained any snippet of the code. But if you have any doubt or didn't understand anything then please do comment in the comment box below and I will be glad to help you.

Please do comment if I have made any typo or if you have a better/different solution other than the one stated above. Feel free to ask me anything related.

You can also contact me if you want to.

Thank you. Have a nice day😃.

Project Euler Problem 67 Solution with Python

Maximum path sum II By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23. 3 7 4 2 4 6 8 5 9 3 That is, 3 + 7 + 4 + 9 = 23. Find the maximum total from top to bottom in triangle.txt (right click and 'Save Link/Target As...'), a 15K text file containing a triangle with one-hundred rows.

Problem 60 Project Euler Solution with python

Prime pair sets The primes 3, 7, 109, and 673, are quite remarkable. By taking any two primes and concatenating them in any order the result will always be prime. For example, taking 7 and 109, both 7109 and 1097 are prime. The sum of these four primes, 792, represents the lowest sum for a set of four primes with this property. Find the lowest sum for a set of five primes for which any two primes concatenate to produce another prime. This problem is j u st a brute force problem. If you have come here because you don't know the limit upto which you will h ave to gener ate the prime numbers t hen go ahe ad and t r y with 10,000 . When I first start ed solving the problem I chose 1 million(beca use most of the problem s on project E uler have this limit ), but it took very long for the computer to fin d the solution. After searching on the internet then I found many people choosing 10, 000 so I have changed my in put f rom 1 million to 10000 and the output was f ast. He...

Project Euler Problem 66 Solution with python

Diophantine equation ¶ Consider quadratic Diophantine equations of the form: $$ x^{2} – Dy^{2} = 1 $$ For example, when $D = 13$, the minimal solution in $ x $ is $ 649^{2} – 13 \times 180^{2} = 1 $ It can be assumed that there are no solutions in positive integers when $ D $ is square. By finding minimal solutions in $ x $ for $ D = {2, 3, 5, 6, 7} $, we obtain the following: $$ 3^{2} – 2×2^{2} = 1 $$ $$ 2^{2} – 3×1^{2} = 1 $$ $$ 9^{2} – 5×4^{2} = 1 $$ $$ 5^{2} – 6×2^{2} = 1 $$ $$ 8^{2} – 7×3^{2} = 1 $$ Hence, by considering minimal solutions in $ x $ for $ D ≤ 7 $, the largest $ x $ is obtained when $ D = 5 $. Find the value of $ D ≤ 1000 $ in minimal solutions of $ x $ for which the largest value of $ x $ is obtained.

RADIUS OF CIRCLE

Search This Blog