Problem 45 Project Euler Solution with python

Triangular, pentagonal, and hexagonal

Triangle, pentagonal, and hexagonal numbers are generated by the following formulae:

Triangle	T_n=n(n+1)/2	1, 3, 6, 10, 15, ...
Pentagonal	P_n=n(3n−1)/2	1, 5, 12, 22, 35, ...
Hexagonal	H_n=n(2n−1)	1, 6, 15, 28, 45, ...

It can be verified that T₂₈₅ = P₁₆₅ = H₁₄₃ = 40755.
Find the next triangle number that is also pentagonal and hexagonal.

A very easy problem if you know the condition to check if the given number is Pentagonal Number and Hexagonal Number. We have used while loop to arrive at the solution.

There is no big algorithm used in this program. You can go see the program and understand it simply.

Program

File: pep45.py ------------------------- # http://radiusofcircle.blogspot.com # time module import time # time at the star of program execution start = time.time() def is_pentagonal(p): """function to check if the given number is pentagonal""" if (1+(24*p+1)**0.5) % 6 == 0: return True return False def is_hexagonal(h): """function to check if the given number is hexagonal""" if (1+(8*h+1)**0.5) % 4 == 0: return True return False # iterator start after 285 i = 286 # while loop for iterating while True: triangle = i*(i+1)/2 if is_pentagonal(triangle) and is_hexagonal(triangle): print triangle break i += 1 # time at the end of program execution end = time.time() # total time taken for execution print end - start

You can download the above source code from Github Gist pep45.py

Output

Summary

It just took a few seconds for me to write the program. I am satisfied with the solution. I have not tried to optimize the code to improve the performance because the program is very fast anyways. I think there is some scope to improve the present solution. You can improve the program if you want to. Please do share it with me if you have written a new solution.

As always you can comment in the comment box below if you have any doubt or didn't understand anything. I will be glad to help you.

Please do comment in the comment box below if you have found any typo or have a different program or a better program or have any suggestion. I will be very happy to view each of them.

You can also contact me.

Thank you. Have a nice day😃!

Making a quiz web app with python and flask

Edit : When you are creating a web app with h tml templates, then y ou will have to sa ve the html file in templates folder in the Current Wor ki ng Directory( CWD). If you save the file in the C W D directl y you will get a TemplateNotFound error. Thank you Udhay for pointing it out. In this post we will create a quiz website using python . I will be using the flask framework . After reading this tutorial you will learn form submission , flask templates , python code in flask templates , shuffling the questions and options with the random module and few others. Please note that this tutorial is not big as it seems to be. Some of the code has been rewritten to maintain consistency and also font size is somewhat big so that your eyes won't get stressed reading this tutorial. Also the content has not occupied the full width of the page. In this tutorial I am assuming that you are having a very basic understanding of the flask framework . Please refer the documentation

Problem 11 Project Euler Solution with python

Largest product in a grid In the 20×20 grid below, four numbers along a diagonal line have been marked in red. 08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08 49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00 81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65 52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91 22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80 24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50 32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70 67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21 24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72 21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95 78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92 16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57 86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58 19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40 04 52 08 83 97 35 99 16 07

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

RADIUS OF CIRCLE

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