Project-Euler | PE's Math Library | Math library

I solving Problem 18 on Project Euler and have written the code for it as below:

Hello,

Question -- Problem 94, Project Euler -- Python -- Almost equilateral triangles

It is easily proved that no equilateral triangle exists with integral length sides and integral area. However, the almost equilateral triangle 5-5-6 has an area of 12 square units. We shall define an almost equilateral triangle to be a triangle for which two sides are equal and the third differs by no more than one unit. Find the sum of the perimeters of all almost equilateral triangles with integral side lengths and area and whose perimeters do not exceed one billion (1,000,000,000).

Output: 518408346

I have a very inneficient solution and it is as follows:

1. I tried to bruteforce(it took a considerable amount of time)(using a for loop)
2. Then I added in the condition to check whether it was a triangle(sum of two sides is greater than the third)
3. Next, I defined the values in a perimeter variable and also used simple geometry for the area variable
4. Next, to check whether they were valid, for the perimeter I used a type method to check whether it was int and since i couldn't do the same for area(since even if it was an integer, it would be part of the float class), I used modulo 1 == 0 to check if it was an integer
5. If it satisfied the condition, i added it to my final 'sum of perimeter' variable. *The code is as follows: *

I was recently playing with problem 14 of the Euler project: which number in the range 1..1_000_000 produces the longest Collatz sequence?

I'm aware of the issue of having to memoize to get reasonable times, and the following piece of Python code returns an answer relatively quickly using that technique (memoize to a dict):

I am going through a solution to the "Pyramid Slide Down" problem (https://www.mathblog.dk/project-euler-18/) and I need help understanding more intuitively the logic behind the solution for updating an index variable in the inner loop.

The algorithm:

Edit: I found the issue: I have not accounted for when multiples of 3 and 5 match! Any hints on how to eliminate the duplicate numbers?

I'm trying to solve the first problem of the Euler Problems from Free Code camp: Multiples of 3 and 5 https://learn.freecodecamp.org/coding-interview-prep/project-euler/problem-1-multiples-of-3-and-5

The problem is this: Find the sum of all the multiples of 3 or 5 below the provided parameter value number.

When I look at my code, it works for the case of 10, but not any of the others. I have looked, tried another option but can not find the issue. Here is what I did.

My Thought Process and current implementation of task

1. Made a loop listing all numbers until the parameter number
2. Made two while loops one for multiples of 3 and one for multiples of 5

3. In each while loop I wanted to continuously add the multiplier (3 or 5) until the num is less than the total of threes or fives I had to add +3 and +5 so the last number in the total array would not go over num

4. I then took the total array and implemented the reduce function to get the sum of the threes and fives totals

Note: I am able to get an array of the values. In the case of 10, I got [3, 6, 9, 5]

My Code

I am trying to go through SICP using Racket and Project Euler as reference for practice. This question is in regards to problem 4 (https://projecteuler.net/problem=4), hence:

A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 × 99. Find the largest palindrome made from the product of two 3-digit numbers.

I am currently still on Chapter 1 (SICP) and loops have not been covered yet, as I see most solutions use. My code runs out of memory every time I try to execute (I have been stuck on this for hours - https://github.com/polila/Project-Euler/commits?author=polila&since=2018-03-19T04:00:00Z&until=2018-03-20T04:00:00Z) LOL.

What I am trying to do is use a recursive procedure by the process of linear iteration (at least that's what I think) - so in my mind it was something like this, where a and b are the max limit of n-digit:

I have created a spider to scrape problems from projecteuler.net. Here I have concluded my answer to a related question with

I launch this with the command scrapy crawl euler -o euler.json and it outputs an array of unordered json objects, everyone corrisponding to a single problem: this is fine for me because I'm going to process it with javascript, even if I think resolving the ordering problem via scrapy can be very simple.

But unfortunately, ordering items to write in json by scrapy (I need ascending order by id field) seem not to be so simple. I've studied every single component (middlewares, pipelines, exporters, signals, etc...) but no one seems useful for this purpose. I'm arrived at the conclusion that a solution to solve this problem doesn't exist at all in scrapy (except, maybe, a very elaborated trick), and you are forced to order things in a second phase. Do you agree, or do you have some idea? I copy here the code of my scraper.

Spider:

I was trying to solve Project Euler's 25th (https://projecteuler.net/problem=25) problem in Swift and got a pretty cryptical error message when I changed my condition in the while loop.

At first, I started with 2, and then 10 and got the right results. But then with 100, the program crashed.

so , I solved a problem online where I found the Largest product of any 5 consecutive numbers In a 1000-digit number :