I completed many of them when I was first learning to code. If all of the permutations are listed numerically or alphabetically, we call it lexicographic order. 01 seconds on an Intel® Core™ i7-2600K CPU @ 3. Although mathematics will help you arrive at elegant and efficient methods, the use of a computer and programming skills will be required to solve most problems. 22 seconds on an Intel® Core™ i7-2600K CPU @ 3. 01 seconds on an Intel® Core™ i7-2600K CPU @ 3. Note: gcd ( x, y) denotes the greatest common divisor of x and y. Benchmark. Link to Project Euler problem 74 The number 145 is well known for the property that the sum of the factorial of its digits is equal to 145: 1! + 4! + 5! = 1 + 24 + 120 = 145 Perhaps less well known is 169, in that it produces the longest chain of numbers that link back to 169; it turns out that there are only three such loops that exist:And finally, start testing: def test_triangles (): triangles = generate_triangles (100000) for i in triangles: if get_factors (i) > 499: return i. freeCodeCamp. Just like when we count up using numbers, we try to modify the rightmost elements and leave the left side. Problem 59: XOR decryption. A palindromic number reads the same both ways. At the start of the walk, a seed is placed on each square. The problems archives table shows problems 1 to 853. 01 seconds on an Intel® Core™ i7-2600K CPU @ 3. 01 seconds on an Intel® Core™ i7-2600K CPU @ 3. There are eight coins in general circulation: 1p, 2p, 5p, 10p, 20p, 50p, £1 (100p), and £2 (200p). {"payload":{"allShortcutsEnabled":false,"fileTree":{"":{"items":[{"name":"hackerrank","path":"hackerrank","contentType":"submodule","submoduleUrl":null. List fact n = product [n, n-1 . The motivation for starting Project. Benchmark. The question is. The correct solution to the original Project Euler problem was found in less than 0. Peak memory usage was about 8 MByte. We need to double 30 and 210 for input (5) and. 40GHz. 0. It is a common recreational problem to make a target number using a selection of other numbers. If Euler's totient function is denoted as φ (n), find the value of n, 1 < n < 10^7, for which φ (n) is a permutation of n and the ratio n/φ (n) produces a minimum. It is possible to write ten as the sum of primes in exactly five different ways: 7 + 3. 3. Since its creation in 2001 by Colin Hughes, Project Euler has gained notability and popularity. At the start of the walk, a seed is placed on each square. Problem 24. 2 days ago · Altcoins. 360 seconds in Python 2. 980479. The correct solution to the original Project Euler problem was found in less than 0. Ask Question Asked 6 years, 5 months ago. The arithmetic sequence, 1487, 4817, 8147, in which each of the terms increases by 3330, is unusual in two ways: (i) each of the three terms are prime, and, (ii) each of the 4-digit numbers are permutations of one another. . 40GHz. {"payload":{"allShortcutsEnabled":false,"fileTree":{"":{"items":[{"name":"hackerrank","path":"hackerrank","contentType":"submodule","submoduleUrl":null. Project Euler #10: Summation of primes. The correct solution to the original Project Euler problem was found in less than 0. 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. During the weekend of Friday 24 September 2021, Project Euler is moving to a new server. For example, 3124 is one possible permutation of the digits 1, 2, 3 and 4. As a. Move from left to right, starting at the index values 0,1 of set_list, flip the value of set_list [index] with. ago. A palindromic number reads the same both ways. 91%. Code Issues Pull requests Problems of Project Euler for anyone interested in improving their programming skills in the form of challenging mathematical problems. I didn’t get the same results as the test case, but the differences are apparent. An example question: Having three black objects B and one white object W they can be grouped in 7. Benchmark. Project Euler Steven Miller ([email protected]. What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?" And I'm wondering if my code to solve this problem is good and if there are ways to make it better. Use this link to get the Project Euler 44 Solution Python 2. list. To associate your repository with the project-euler-python-solutions topic, visit your repo's landing page and select "manage topics. One Pair: Two cards of the same value. java","path. This solution contains 16 empty lines, 24 comments and 2 preprocessor commands. 23, 2023 — Training Time:. Sep 6, 2011 at 10:24 $egingroup$ @Hannesh I know, but I was talking about a more general algorithm that counts the digits, not one that checks whether a number is within a certain range. The sum of these multiples is 23. So on the 20x20 it takes 40 steps. If you would like to tackle the 10 most recently published problems, go to Recent problems. Project Euler is a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve. e. 02 seconds on an Intel® Core™ i7-2600K CPU @ 3. What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?" And I'm wondering if my code to solve this problem is good and if there are ways to make it better. 40GHz. This solution contains 12 empty lines, 13 comments and 6 preprocessor commands. If p is the perimeter of a right angle triangle with integral length sides, { a, b, c }, there are exactly three solutions for p = 120. 40GHz. Although mathematics will help you arrive at elegant and efficient methods, the use of a computer and programming skills will be required to solve most problems. 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. The correct solution to the original Project Euler problem was found in 0. Find the sum of all numbers below which divide the sum of the factorial of their digits. NOTE: If you have forgotten your password, we are unable to help recover accounts if you have signed in at. A permutation is an ordered arrangement of objects. 1. The problem is: 145 is a curious number, as 1! + 4! + 5! = 1 + 24 + 120 = 145. This solution contains 7 empty lines, 10 comments and 2 preprocessor commands. And a lot of people have already publicly accepted the challenge. And there's even more fun (and knowledge) to be had when discussing the specifics of a solution. 40GHz. Project Euler is not great for learning about programming. 40 GHz, 64-bit CPU running Windows 7, 8 GB RAM, Enthought python ). 40GHz. 1. So I am working on Project Euler #23, and I need some efficiency assistance. list (itertools. 40GHz. @anoeto - if the matrix is n x n, can you show a more complicated example - e. Problem 24: Lexicographic permutations Problem 25: 1000-digit Fibonacci number Problem 26: Reciprocal cycles Problem 27: Quadratic primes Problem 28: Number spiral diagonals Problem 29: Distinct powers One of the best way is to generate two numbers a,b and generate the third number with the condition c = a-b . 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. 40GHz. by inhahe » Sat Aug 25, 2007 9:45 pm. What is the sum of the digits of the number 2^1000? Updated: Nov. ----- Code and ResourcesFull code from the video is on ou. This solution contains 18 empty lines, 17 comments and 12 preprocessor commands. If you would like to tackle the 10 most recently published problems, go to Recent problems. while flag:Project Euler is a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve. 1The constants in this solution are from the formula: t = n * log10 (phi) + log10 (1/sqrt (5)). A permutation is an ordered arrangement of objects. Peak memory usage was about 26 MByte. key point. 2 and 3. Project Euler #8: Largest product in a series. 1. Friends - Project Euler - #24 Lexicographic Permutations - Project Euler * E — C!1 X ' Logged 'assahil200495597 iject Elller H, mm 2323 01:53 3* Q A About Recent Progress Account News Friends Statistics 4- -> Lexicographic Permutations Problem 24 f é: a A permutation is an ordered arrangement of objects. 145 is a curious number, as 1! + 4! + 5! = 1 + 24 + 120 = 145. For example, 200 = 5 2 2 3 or 120072949 = 23 2 61 3. Therefore, probably it requires a deep knowledge of mathematics. My times ( in milliseconds ) are below ( on an Intel i5-2430M @ 2. 10 Replies 4223 Views Last post by kkm000 Mon Jul 17, 2023 3:31 am; 634 topicsMarch 24, 2020 10:49. 40GHz. Sep 6,. Solution of “Pell’s Equation” by Chakravala Method by Gopal Menon. " GitHub is where people build software. Although mathematics will help you arrive at elegant and efficient methods, the use of a computer and programming skills will be required to solve most problems. Project Euler ( projecteuler. group-theory; project-euler; A little mouse on the pampas. g. Easy Max Score: 100 Success Rate: 74. Find the sum of all numbers which are equal to the sum of the factorial of their digits. Level. if the sum is equal to the original number then add it to our result. Improve your writing skills in 5 minutes a day with the Daily Writing Tips email newsletter. Although mathematics will help you arrive at elegant and efficient methods, the use of a computer and programming skills will be required to solve most problems. First, a a standard prime sieve finds all prime numbers up to our limit (1000000 by default) and keeps them in a std::set. 01 seconds on an Intel® Core™ i7-2600K CPU @ 3. (compiled for x86_64 / Linux, GCC flags: -O3 -march=native -fno-exceptions -fno-rtti -std=gnu++11 . 1. What is remarkable is that, by using the same digital substitutions, the anagram, RACE, also forms a square number: 9216 = 96^ (2). A palindromic number reads the same both ways. Solution of Project Euler problems. This solution contains 8 empty lines, 9 comments and 2 preprocessor commands. Project Euler 28 Solution: Number spiral diagonals. 16 seconds on an Intel® Core™ i7-2600K CPU @ 3. Although no one has proved it yet, it is thought that some numbers, like 196, never. 1. Project Euler - Problem 24: Lexicographic permutations. prob. This solution contains 20 empty lines, 20 comments and 6 preprocessor commands. The correct solution to the original Project Euler problem was found in 0. 01 seconds on an Intel® Core™ i7-2600K CPU @ 3. 5 for p in range (4): lastnum += increment total += lastnum count += 1 return total. Problem 24. 01 seconds on an Intel® Core™ i7-2600K CPU @ 3. Benchmark. Once you have registered you can switch between unlisted (private) and public status at any time from your Account page. is a curious number, as which is divisible by . Find the sum of all numbers which are equal to the sum of the factorial of their digits. So yes, if you're going to solve the problem, you are going to have. This was my idea. Problem #25 from Project Euler asks:. {"payload":{"allShortcutsEnabled":false,"fileTree":{"":{"items":[{"name":"hackerrank","path":"hackerrank","contentType":"submodule","submoduleUrl":null. For each of these steps I have to check whether enough neighbor exist. Starting with the number 1 and moving to the right in a clockwise direction a 5 by 5 spiral is formed as follows: It can be verified that the sum of the numbers on the diagonals is 101. If all of the permutations are listed numerically or alphabetically, we call it lexicographic order. " EG the product of the first four adjacent digits is 7 * 3 * 1 * 6. I scored 13526 points (out of 15700 possible points, top rank was 17 out of ≈60000 in August 2017) at Hackerrank's Project Euler+. 0 answers. The correct solution to the original Project Euler problem was found in less than 0. Social Media Remind Me The Project Euler solutions to the first 100. 9. {"payload":{"allShortcutsEnabled":false,"fileTree":{"":{"items":[{"name":"Project Euler #1 Multiples of 3 and 5. Project Euler - Rust. Calculate the abundant numbers till the limit. Here's the code: import numpy as np s = '''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. To associate your repository with the project-euler topic, visit your repo's landing page and select "manage topics. Cho đến tháng 7 năm 2023, Project Euler có hơn 840 bài. A permutation is an ordered arrangement of objects. Project Euler is a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve. 5 + 1. 40GHz. Cheating way: Using itertools module this problem is reduced to a one-liner. My solution is below. 1k 1 1 gold badge 49 49 silver badges 82 82 bronze badges $endgroup$ Add a comment |. Title. An another approach might be to stop the looping once you have found out the solution, because it is given in the question that there is only one such solution. 145 is a curious number, as 1! + 4! + 5! = 1 + 24 + 120 = 145. Project Euler 2 python3. $endgroup$ – Paul Manta. Although mathematics will help you arrive at elegant and efficient methods, the use of a computer and programming skills will be required to solve most problems. #2. Project Euler #5: Smallest multiple. Here is the link for the code - Euler # 24 Lexicographic permutations in Python. Solved By. Brute force;. The arithmetic sequence, 1487, 4817, 8147, in which each of the terms increases by 3330, is unusual in two ways: (i) each of the three terms are prime, and, (ii) each of the 4-digit numbers are permutations of one another. ago. Euler Network’s achievement of raising $3 million in a 24-hour presale stands out as a testament to its strategic approach and the community’s confidence in its vision. Benchmark. 3. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 × 99. gitignore","contentType":"file"},{"name":"001. For example, 3124 is one possible. A coding challenge site. And finally the greatest product is printed. 12 seconds on an Intel® Core™ i7-2600K CPU @ 3. Project Euler 34 Solution: Digit factorials. Though the problem is more on figuring out the mathematical insight, this post will focus on the engineering side. The Pythagorean Theorem gives us: a 2 + b 2 = c 2 and by intuition a + b + c = p (perimeter). The 310 solved problems (that's level 12) had an average difficulty of 32. First, generate four million pseudo-random numbers using a specific form of what is known as a "Lagged Fibonacci Generator": For 1 ≤ k ≤ 55. Here we'll discuss, analyze, and code a solution for Project Euler #24: Lexicographic Permutations. I'm trying to learn the basics of C++ by going through some Project Euler problems. gitignore","path":". In fact, he learned several different languages on the spot, like parts of Bash and PHP. {"payload":{"allShortcutsEnabled":false,"fileTree":{"":{"items":[{"name":"hackerrank","path":"hackerrank","contentType":"submodule","submoduleUrl":null. Multiples of 3 or 5. Easy Max Score: 100 Success Rate: 93. (compiled for x86_64 / Linux, GCC flags: -O3 -march=native -fno-exceptions -fno-rtti -std=gnu++11 . Project Euler 66 Solution Runs 0. (compiled for x86_64 / Linux, GCC flags: -O3 -march=native -fno-exceptions -fno-rtti -std=gnu++11 -DORIGINAL ) See here for a comparison of all solutions. While looking at the ability of GPT-4 to solve programming puzzles, I asked GPT-4 to write a solution program to Project Euler problem 1 (Find the sum of all the multiples of 3 or 5. {"payload":{"allShortcutsEnabled":false,"fileTree":{"":{"items":[{"name":"Project Euler #10: Summation of primes","path":"Project Euler #10: Summation of primes. Learn to Code — For Free. 40GHz. The motivation for starting Project. Benchmark. My C++ solution for Project Euler 24: Lexicographic permutations <<. (and if you're too lazy to find the solution yourself, googling project euler problem 34 and you'll find plenty of answer in blogs). (compiled for x86_64 / Linux, GCC flags: -O3 -march=native -fno-exceptions -fno-rtti -std=gnu++11 . Problem 74. A website dedicated to the fascinating world of. 6. Although mathematics will help you arrive at elegant and efficient methods, the use of a computer and programming skills will be required to solve most problems. May 29, 2017 at 23:24. One Pair: Two cards of the same value. Note: as 1! = 1 and 2! = 2 are not sums they are not included. If all of the permutations are listed numerically or alphabetically. This problem is a programming version of Problem 24 from projecteuler. Project Euler 87 Solution last updated January 24, 2016. Problems. Benchmark. You can find my full solution here. . We can also use the formula that the sum of the first n integers is n n+1 2. Euler Network’s achievement of raising $3 million in a 24-hour presale stands out as a testament to its strategic approach and the community’s confidence in its vision. flag = True i = 1. 99%. If you can solve. To associate your repository with the projecteuler-solutions topic, visit your repo's landing page and select "manage topics. Multiples of 3 or 5. Peak memory usage was about 13 MByte. ago. The correct solution to the original Project Euler problem was found in 0. Project Euler #329 (Prime Frog) - Stochastic independence. emergency account recovery key, then you can use it to recover your account. If all of the permutations are listed numerically or alphabetically, we call it lexicographic order. The 310 solved problems (that's level 12) had an average difficulty of 32. Solve Challenge. 16 seconds on an Intel® Core™ i7-2600K CPU @ 3. That is, 349 took three iterations to arrive at a palindrome. What sets Euler apart is its commitment to innovation, rapid development, and a comprehensive ecosystem strategy that goes beyond the typical blockchain project. Project Euler 34 - digit factorials. It was solved by 95,102 people as of September 1, 2021. A permutation is. Solution to Project Euler Problem 16: Power digit sum - 2^15 = 32768 and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26. (compiled for x86_64 / Linux, GCC flags: -O3 -march=native -fno-exceptions -fno-rtti -std=gnu++11 . The motivation for starting Project. If all of the permutations are listed alphabetically, we call it lexicographic order. We use this and inclusion/exclusion to quickly get a formula for the sum of all multiples of 3 and 5 up to 1000. Leonhard Euler was born on 15 April 1707. We will use the sequence (0, 1, 2, 5, 3, 3, 0) as a running example. The first five squbes are 72, 108, 200, 392, and 500. The number 6 can be written as a palindromic sum in exactly eight different ways: (1,1,1,1,1,1), (1,1,2,1,1), (1,2,2,1), (1,4,1), (2,1,1,2), (2,2,2), (3,3), (6) We shall define a twopal to be a palindromic tuple having at least one element with a value of 2. 1. This is problem 4 from the Project Euler. In the dynamic world of cryptocurrencies, fundraising strategies play a pivotal role in determining a project’s success. The arithmetic derivative is defined by. Project Euler 26 Solution: Reciprocal cycles. Solve Challenge. 1,188 7 8. It includes over 850. 24 stars Watchers. 40GHz. Project Euler is a website created back in 2001. 3. For example, 3124 is one possible permutation of the digits 1, 2, 3 and 4. 15 seconds on an Intel® Core™ i7-2600K CPU @ 3. NOTE: If you have forgotten your password, we are unable to help recover accounts if you have signed in at. Written By Ritika Trikha | May 1, 2015 Last weekend, HackerRank hosted. 1. Extended to solve all test cases for HackerRank Project Euler 24. Benchmark. The motivation for starting Project. Here we'll discuss, analyze, and code a solution for Project Euler #24: Lexicographic Permutations. To associate your repository with the project-euler-c-solutions topic, visit your repo's landing page and select "manage topics. The project attracts graduates and students interested in mathematics and computer programming. WASM Specific. What is Octave? Octave is a free high-level interpreter language that is equivalent to the textuelle programming language MATLAB. The ‘reverse’ diagonal is defined as bottom-left to top-right when viewed in the C-array style convention. Although mathematics will help you arrive at elegant and efficient methods, the use of a computer and programming skills will be required to solve most problems. The correct solution to the original Project Euler problem was found in 0. The correct solution to the original Project Euler problem was found in less than 0. If all of the permutations are listed numerically or alphabetically, we call it lexicographic order. It was created by Colin Hughes in 2001 and has since become a popular platform for individuals to test and improve their mathematical and programming abilities. 5,580; asked Apr 27, 2020 at 7:32. 1] recur :: Int -> Int -> [Int] -> [Int] recur x y arr | y > 1 = arr !! d : recur r (y-1. Benchmark. HackerRank version. Title. g. Project Euler #34 Digit factorials. 2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder. By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13. I have the following problem (from ProjectEuler. if you check Fibonacci series, for even numbers 2 8 34 144 610 you can see that there is a fantastic relation between even numbers, for example: 34 = 4*8 + 2, 144 = 34*4 + 8, 610 = 144*4 + 34; this means that next even in Fibonacci can be expressed like below. The algorithm. The solutions provided in this repository can be found for the respective challenges on the HackerRank Project Euler+ page. It's called #ProjectEuler100. 1 I am trying to solve the problems from Project Euler using Haskell, but I. Project Euler is a series of coding challenges that have been popular for many years. The correct solution to the original Project Euler problem was found in less than 0. A laborious ant walks randomly on a 5x5 grid. (compiled for x86_64 / Linux, GCC flags: -O3 -march=native -fno. Project Euler 1 - Multiples of 3 and 5 by Loki. 40GHz. We shall define a sqube to be a number of the form, p2q3, where p and q are distinct primes. 1. At the speed my code is currently running that will take like a billion years. {"payload":{"allShortcutsEnabled":false,"fileTree":{"":{"items":[{"name":"hackerrank","path":"hackerrank","contentType":"submodule","submoduleUrl":null. This said, the first 100 problems are totally do-able by a new developer. 2. Easy Max Score: 100 Success Rate: 93. {20,48,52}, {24,45,51}, {30,40,50} For which value of p ≤ 1000, is the number of solutions maximised? Analysis. Project Euler 26 Definition. 1. A place to air possible concerns or difficulties in understanding ProjectEuler problems. Discussions. This is just a short blog post to raise some awareness to some fun programming and mathematical challenges I recently came across, hosted on Project Euler. (3) 0. However, when n = 40, 402 + 40 + 41 = 40 (40 + 1) + 41 is divisible by 41, and certainly when n = 41, 41² + 41 + 41 is clearly divisible by 41. sequence import Factorials def solve(): """ Compute the answer to Project Euler's problem #34 """ min_digits = 2 max_digits = 7 # Avoid re-computing various digit factorials - pre-compute for all decimal digits factorial. This solution contains 24 empty lines, 30 comments and 12 preprocessor commands. net. 01 seconds on an Intel® Core™ i7-2600K CPU @ 3. A permutation is an ordered arrangement of objects. Benchmark. 3. This solution contains 11 empty lines, 13 comments and 2 preprocessor commands. What is the sum of the numbers on the diagonals in a 1001 by 1001 spiral formed in the same way?This solution contains 13 empty lines, 14 comments and 1 preprocessor command. 2. Updated Oct 24, 2022; Java; cr2007 / Project-Euler Star 4. For example, 3124 is. Starting with the number 1 and moving to the right in a clockwise direction a 5 by 5 spiral is formed as follows: It can be verified that the sum of the numbers on the diagonals is 101. freeCodeCamp - Project Euler with Rust Course Desciption. 00%. Cheating way: Using itertools module this problem is reduced to a one-liner. {"payload":{"allShortcutsEnabled":false,"fileTree":{"":{"items":[{"name":". Project Euler 87 Solution Runs 0. 806. (compiled for x86_64 / Linux, GCC flags: -O3 -march=native -fno-exceptions -fno-rtti -std=gnu++11 . {"payload":{"allShortcutsEnabled":false,"fileTree":{"":{"items":[{"name":". const unsigned int factorials[] = { 1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880 }; // no more than 7*9! = 2540160 for the original problem: unsigned int limit; std. 1. Thank you!This is Project Euler Problem 11In the 20 × 20 grid below, four numbers along a diagonal line have been marked in red. 40GHz. gitignore","path":". Project Euler RStats. If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. 210 seconds in Python 2. How to solve this problem 710 of Project-Euler. To keep with the spirit of Project Euler, each solution after the first 100 problems is encrypted with its corresponding answer. Even (n)=4*Even (n-1)+E (n-2);I am aware of this is one of the last questions of the Euler Project. 01 seconds on an Intel® Core™ i7-2600K CPU @ 3. Benchmark. Spoilers ahead. If you would like to tackle the 10 most recently published problems, go to Recent problems. This makes SPOJ solutions a little more complex than Project Euler solutions, but the syntax is usually pretty straight forward. Bắt đầu hoạt động. python c project-euler math programming-challenge ada Updated Sep 24, 2022; C; Load more… Improve this page Add a description, image, and links to the project-euler topic page so that developers can more easily learn about it. Project Euler 54: In the card game poker, a hand consists of five cards and are ranked, from lowest to highest, in the following way: High Card: Highest value card. 7 source. GitHub community articles Repositories. 6% at Project Euler and I scored 13526 points (out of 15700 possible points, top rank was 17 out of ≈60000 in August 2017) at Hackerrank's Project Euler+ . Benchmark. $endgroup$ – user2336315. Project Euler+ is a series of challenging mathematical and computational programming problems hosted on HackerRank. admit8490 September 12, 2022, 2:35pm 2. Learn to Code — For FreeDuring this time Project Euler will be taken offline and the website will not be accessible. 12 would fit the bill. system Closed March 14, 2023, 2:36am 3. Perhaps less well known is 169, in that it produces the longest chain of numbers that link back to 169; it turns out that there are only three such loops that exist: 169 → 363601 → 1454. diagonal_reverse (grid, run_len) ¶. Move from left to right, starting at the index values 0,1 of set_list, flip the value of set_list [index] with.