Skip to main content

Problem 33 Project Euler Solution with Python

Digit cancelling fractions

The fraction 49/98 is a curious fraction, as an inexperienced mathematician in attempting to simplify it may incorrectly believe that 49/98 = 4/8, which is correct, is obtained by cancelling the 9s.
We shall consider fractions like, 30/50 = 3/5, to be trivial examples.
There are exactly four non-trivial examples of this type of fraction, less than one in value, and containing two digits in the numerator and denominator.
If the product of these four fractions is given in its lowest common terms, find the value of the denominator.

 This problem is very simple if you were to solve it with the help of python. In python you will have to use a module to deal with fractions. It is called fractions module. It is so simple to learn and you can see the documentation: fractions - Rational Numbers.

Please go and have a look at the official documentation and you will see its simplicity.

 If you will understand the fractions module then you can directly have a look at the code, because there is no big algorithm to understand.

Program 

As given in the question the value of the fractions which will have the given qualities have a value less than 1(denominator > numerator). The same can be seen in the second for loop.

 I have used Python sets to find the common element and I am assuming that you should be familiar with everything if you have given a look at fractions module.

 To perfectly understand the program I recommend you to take a few examples and substitute the values in the code to see what is happening in the background.

 A few examples you will have to try are49/98,59/68,89/99,30/40,12/20 .Try to evaluate each and every statement if it is necessary or not. Then I am sure you will for sure understand the code.

 As always if you want to download the above source code then you can download it from Github Gist pep33.py

 Output


Summary

This problem was relatively easy and I don't have any extra comments on this problem. I would have had any extra comments if I had not solved the problem with Python. Thanks to python, its inbuilt fraction module has helped me solve the problem easily.

 If you have any doubt or didn't understand anything then comment in the comment box below and I will be glad to help you.

 Please do comment if you have found any typo or have a better program or have a different program or have any suggestions. I will be glad to view each and every one of them.

 You can also contact me.

Thank you. Have a nice day😃.
Labels:

Popular posts from this blog

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
Read more

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
Read more

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
Read more