Project Euler ( projecteuler. Problem 1: Multiples of 3 or 5 2. Modified 6 years, 5 months ago. (compiled for x86_64 / Linux, GCC flags: -O3 -march=native -fno-exceptions -fno-rtti -std=gnu++11 . You can use the n choose r formula to solve it: n!/r! (n-r)! r = the number of rows which is 20, and n is 2r which is 40. 2 days ago · Euler Network (EUL), a project with revolutionary potential, hopes to. 980797. edu) (*For this problem we could go through and keep track of the multiples of 3 and 5 and add. The process will commence on Friday, 3 February 2023 at 22:00 (BST) and it is estimated to take 6-8 hours. 2. 0. Find the sum of all numbers which are equal to the sum of the factorial of their digits. 99%. Find ∑ gcd ( k, k ′) for 1 < k ≤ 5 × 10 15. A laborious ant walks randomly on a 5x5 grid. g. The question is. {"payload":{"allShortcutsEnabled":false,"fileTree":{"":{"items":[{"name":"hackerrank","path":"hackerrank","contentType":"submodule","submoduleUrl":null. Project Euler is a series of challenging mathematical and computational problems that require creative problem-solving and programming skills to solve. 40GHz. Project Euler Python. That is, 349 took three iterations to arrive at a palindrome. What is remarkable is that, by using the same digital substitutions, the anagram, RACE, also forms a square number: 9216 = 96^ (2). Summing everything The correct solution to the original Project Euler problem was found in less than 0. This is a great way to get started with Test Driven Development. Even Fibonacci Numbers. (compiled for x86_64 / Linux, GCC flags: -O3 -march=native -fno-exceptions -fno-rtti -std=gnu++11 . 40GHz. // As stated in the problem, 1 = 1! and 2 = 2! are excluded. A permutation is an ordered arrangement of objects. Since you're learning, I'm assuming you don't want an explicit answer to this. The 2×2×2 variant has 8 cubelets with a total of 24 visible. 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. If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. I just finished Project Euler problem 9 (warning spoilers ): A Pythagorean triplet is a set of three natural numbers, a < b < c, for which, a^2 + b^2 = c^2 For example, 3^2 + 4^2 = 9 + 16 = 25 = 5^2. The correct solution to the original Project Euler problem was found in 0. This solution contains 8 empty lines, 4 comments and 8 preprocessor commands. Benchmark. 1. More than 100 million people use GitHub to discover, fork, and contribute to over 420 million projects. So on the 20x20 it takes 40 steps. Peak memory usage was about 8 MByte. 13. 1. This website is one of the largest collections of explained Project Euler Solutions, not just code, but detailed explanations of the mathematics and coding I used to solve over 300 problems, with as many interactive tests as possible, to help anyone in need in their Project Euler journey! Furthermore, this website is also, largely, my personal. The ‘reverse’ diagonal is defined as bottom-left to top-right when viewed in the C-array style convention. You can find my full solution here. Problem 14. The algorithm. The objective of Su Doku puzzles, however, is to replace the blanks (or zeros) in a 9 by 9. 5) % 6 == 0: #function to check if the number is pentagonal number or not return True return False. lsp. We are going to look at problem #820, and try to solve it on various kinds of hardwares, ranging from CPU to. (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. This solution contains 13 empty lines, 11 comments and 6 preprocessor commands. Project Euler Problem 24. Find maximum possible value of among all such Pythagorean triplets, If there is no such Pythagorean triplet print . 01 seconds on an Intel® Core™ i7-2600K CPU @ 3. public class Problem23 { /** * A brute force solution - * 1. My solution is below. The decimal representation of the unit fractions with denominators 2 to 10 are given: 0. Euler Network's ongoing presale success, securing an impressive $3 million in just 24 hours without relying on celebrity hype, underscores its potential to disrupt the status quo. A number n is called deficient if the sum. 01 seconds on an Intel® Core™ i7-2600K CPU @ 3. Contribute to muratcorlu/euler development by creating an account on GitHub. During the weekend of Friday 24 September 2021, Project Euler is moving to a new server. sf","path":"Sidef/001 Multiples of 3 and 5 -- v2. The lexicographic permutations of 0, 1 and 2 are: 012 021 102 120 201 210. Closed 10 years ago. Original Problem. (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. 1. Problem 96. Project Euler, ftw! If you solve the first 50–100 Project Euler problems you will: Project Euler is a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve. flag = True i = 1. net/problem=24 ) A permutation is an ordered arrangement of objects. (compiled for x86_64 / Linux, GCC flags: -O3 -march=native -fno-exceptions -fno-rtti -std=gnu++11 . In the dynamic world of cryptocurrencies, fundraising strategies play a pivotal role in determining a project’s success. 2. To associate your repository with the project-euler topic, visit your repo's landing page and select "manage topics. (1) Where 0. For example, the sum of the proper divisors of 28 would be 1 + 2 + 4 + 7 + 14 = 28, which means that 28 is a perfect number. For example, 3124 is one possible. Today’s problem 7 is particularly easy until the test case; to search for the 10001^th prime number. Euler Network's ongoing presale. (compiled for x86_64 / Linux, GCC flags: -O3 -march=native -fno-exceptions -fno-rtti -std=gnu++11 . , and has a 1-digit recurring cycle. A permutation is an ordered arrangement of objects. Project Euler Prob 7 Python. 5 + 1. In the 20 × 20 grid below, four numbers along a diagonal line have been marked in red. 2. This solution contains 8 empty lines, 10 comments and 2 preprocessor commands. Looking at the table below, it is easy to verify that the maximum possible sum of adjacent numbers in any direction (horizontal, vertical, diagonal or anti-diagonal) is 16 ( = 8 + 7 + 1 ). If all of the permutations are listed numerically or alphabetically, we call it lexicographic order. cpp","path":"Project Euler #1 Multiples of 3 and 5. To associate your repository with the projecteuler-solutions topic, visit your repo's landing page and select "manage topics. freeCodeCamp - Project Euler with Rust Course Desciption. For example, 349 + 943 = 1292 1292 + 2921 = 4213 4213 + 3124 = 7337. You can solve them however you want to solve them, I personally did my solutions in code because I was trying to learn Ruby. This solution contains 11 empty lines, 13 comments and 2 preprocessor commands. 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 -DORIGINAL ) See here for a comparison of all solutions. A few remarks on your current code: You should have a look at Python's official style-guide, PEP8. Problem 280: Ant and seeds. admit8490 September 12, 2022, 2:35pm 2. The search box will use Google to perform a search of the Project Euler problem set. 6 is a factor of 24 hence we only look for the candidates 12, 18 and 24 when searching for the. For each of these steps I have to check whether enough neighbor exist. What sets Euler apart is its commitment to innovation, rapid development, and a comprehensive ecosystem strategy that goes beyond the typical blockchain project. (compiled for x86_64 / Linux, GCC flags: -O3 -march=native -fno-exceptions -fno-rtti -std=gnu++11 . Project Euler 24 asks to develop lexicographic. As explained in the problem statement, you can compute all Fibonacci numbers in an iterative way: F_i=F_ {i-2}+F_ {i-1} F i=F i−2+F i−1. This solution contains 9 empty lines, 11 comments and 5 preprocessor commands. More than 100 million people use GitHub to discover, fork, and contribute to over 420 million projects. The function E_116 () has two parameters i = number of black coloured square tiles covered by the new coloured (red, green or blue) tiles and k = total number of black coloured square tiles. The problem. 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. We shall call CARE (and RACE) a square anagram word. 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. (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. Problem 1: Multiples of 3 or 5 2. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 × 99. , if x = 3456 x=3456 then shift = 1000 shif t=1000 . This solution contains 10 empty lines, 16 comments and 3 preprocessor commands. Project Euler is a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve. That's a huge number! The number paqbrc p a q b r c for example has (a + 1)(b + 1)(c + 1) ( a + 1) ( b + 1) ( c + 1) divisors. Solution to Problem 24 on Project Euler. Benchmark. It's more programming for mathematicians than math for programmers, and doing the problems won't increase your algorithmic skills as much as doing Codeforces/competitive programming. To associate your repository with the project-euler-python-solutions topic, visit your repo's landing page and select "manage topics. At each step, the ant moves to an adjacent square at random, without leaving the grid; thus there are 2, 3 or 4 possible moves at each step depending on the ant's position. Share this: Facebook; Twitter; Email; LinkedIn; Discussion. Divisibility by one million is not the same thing as just being larger than one million. Move from left to right, starting at the index values 0,1 of set_list, flip the value of set_list [index] with. The correct solution to the original Project Euler problem was found in less than 0. Problem 24. , if x = 3456 x=3456 then shift = 1000 shif t=1000 . 3. net) is a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve. Problem 34. AnythingApplied • 12 yr. My C++ solution for Project Euler 24: Lexicographic permutations <<. I solved the question in 1 min 32 seconds which is a lot. 1. Even Fibonacci Numbers. 1. HackerRank version. 9. At the start of the walk, a seed is placed on each square. It can take a few minutes to install all the dependencies/tools, on first start. The 12 th term, F 12 = 144, is the first term to contain three digits. I took a walk around the campus after lunch. 40GHz. This is equivalent and more efficient: count = 1 lastnum = 1 total = lastnum while count < (2 * n - 1): increment = count * 0. Project Euler 26 Solution: Reciprocal cycles. (compiled for x86_64 / Linux, GCC flags: -O3 -march=native -fno-exceptions -fno-rtti -std=gnu++11 . 1. 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. A row measuring seven units in length has red blocks with a minimum length of three units placed on it, such that any two red blocks (which are allowed to be different lengths) are separated by at least one grey square. The correct solution to the original Project Euler problem was found in 0. (compiled for x86_64 / Linux, GCC flags: -O3 -march=native -fno-exceptions -fno-rtti -std=gnu++11 . while flag:Project Euler is a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve. 02 seconds on an Intel® Core™ i7-2600K CPU @ 3. Solution of Project Euler problems. This solution contains 24 empty lines, 30 comments and 12 preprocessor commands. org. 01 seconds on an Intel® Core™ i7-2600K CPU @ 3. This solution contains 17 empty lines, 25 comments and 6 preprocessor commands. " GitHub is where people build software. int. Solution Implementation ¶. (compiled for x86_64 / Linux, GCC flags: -O3 -march=native -fno-exceptions -fno-rtti -std=gnu++11 . Extended to solve all test cases for HackerRank Project Euler 24. 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. 1. So Ive been working on project Euler problem #650, and it generates the correct answer for smaller values, but they are looking for the solution to values up to 20,000. There are no arithmetic sequences made up of three 1-, 2-, or 3-digit. Benchmark. The motivation for starting Project. split each number into its digits. 2. {"payload":{"allShortcutsEnabled":false,"fileTree":{"":{"items":[{"name":"hackerrank","path":"hackerrank","contentType":"submodule","submoduleUrl":null. 24 is divisible by 1, 2, 3 and 4. I'm working on project euler problem number eight, in which ive been supplied this ridiculously large number: . Although no one has proved it yet,. This solution contains 9 empty lines, 16 comments and 2 preprocessor commands. Project Euler Problem 24 asks us to find the millionth lexicographic permutation of the numbers 1 through 9. The Digit factorials is Problem 34 in Project Euler. ngày 5 tháng 10 năm 2001. 210 seconds in Python 2. Find the maximum total from top to bottom of the triangle below: NOTE: As there are only 16384 routes, it is possible to solve this problem by trying every route. The correct solution to the original Project Euler problem was found in 0. digital import digits_of from lib. 15 seconds on an Intel® Core™ i7-2600K CPU @ 3. because all those sums would have at most six digits. {"payload":{"allShortcutsEnabled":false,"fileTree":{"":{"items":[{"name":". – fubar. (compiled for x86_64 / Linux, GCC flags: -O3 -march=native -fno-exceptions -fno-rtti -std=gnu++11 . Use this link to get the Project Euler 66 Solution Python 2. Calculate the abundant numbers till the limit. Project Euler, ftw! If you solve the first 50–100 Project Euler problems you will:Project Euler is a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve. This makes SPOJ solutions a little more complex than Project Euler solutions, but the syntax is usually pretty straight forward. In this problem you will be given six numbers and a target number. Cheating way: Using itertools module this problem is reduced to a one-liner. Tests. (compiled for x86_64 / Linux, GCC flags: -O3 -march=native -fno-exceptions -fno-rtti -std=gnu++11 . Solution. List fact n = product [n, n-1 . Project Euler #24: Lexicographic permutations 5 days Problem Submissions. key point. Problem 484. Project Euler is a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve. I will share with you my thought process and two things I learnt today about prime 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. Problem 24: Lexicographic permutations Problem 25: 1000-digit Fibonacci number. Get Help. answered Oct 30, 2017 at 19:24. Contribute to muratcorlu/euler development by creating an account on GitHub. One Pair: Two cards of the same value. Sep 6,. For those of you who don’t know, Project Euler is a series of challenging mathematical/computer programming problems. 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. My username at Project Euler is stephanbrumme while it's stbrumme at Hackerrank. gitignore","path":". Project Euler 28 Solution: Number spiral diagonals. 7. 2. To associate your repository with the project-euler topic, visit your repo's landing page and select "manage topics. 806. And it is my 7^th day! Yay~💪🏻. maksbd19 maksbd19. . This solution contains 23 empty lines, 27 comments and 4 preprocessor commands. Run all problems: cargo build --release cargo run --release --bin euler. This solution contains 12 empty lines, 13 comments and 6 preprocessor commands. Problem 24. prob. 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. So Ive been working on project Euler problem #650, and it generates the correct answer for smaller values, but they are looking for the solution to values up to 20,000. {20,48,52}, {24,45,51}, {30,40,50} For which value of p ≤ 1000, is the number of solutions maximised? Analysis. We shall define a sqube to be a number of the form, p2q3, where p and q are distinct primes. 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. Cho đến tháng 7 năm 2023, Project Euler có hơn 840 bài. 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 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. All tasks are made to be done solo, if you encounter problems you may ask help for a specific mathematical or programming concept, but you can't just decide to ask how to solve the problem at hand - takes away the point of project Euler. Run specific problem: cargo run --release --bin p001. 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. never form a "running crack". Fore re-usability (I know, not such a big concern here) you should. Each character on a computer is assigned a unique code and the preferred standard is ASCII (American Standard Code for Information Interchange). “Project Euler exists to encourage, challenge, and develop the skills and enjoyment of anyone with an interest in the fascinating world of. You are missing the numbers that are divisible by both 3 and 5 (or 15) – Diogenis Siganos. If you would like to tackle the 10 most recently published problems, go to Recent problems. admit8490 September 12, 2022, 2:35pm 2. (compiled for x86_64 / Linux, GCC flags: -O3 -march=native -fno-exceptions -fno-rtti -std=gnu++11 . 40GHz. alphanumeric characters (A-Z, a-z, 0-9), dot (. 5 for p in range (4): lastnum += increment total += lastnum count += 1 return total. net) is a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve. current cell and its three neighbors going right and down. Try it out. The correct solution to the original Project Euler problem was found in less than 0. A perfect number is a number for which the sum of its proper divisors is exactly equal to the number. 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. A place to air possible concerns or difficulties in understanding ProjectEuler problems. 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. 1 million = 1,000,000 = 10^6 = 2^6 * 5^6. The motivation for starting Project. Passwords must contain between 8 and 32 characters. Consider the sequence 1504170715041707 n mod 4503599627370517. 1 I am trying to solve the problems from Project Euler using Haskell, but I. My solution: sum ( [17,305,5473,98209,1762289,31622993,102334155,173045317,197203134,243756479,267914296,314467641. A website dedicated to the fascinating world of. Project Euler is a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve. Note: gcd ( x, y) denotes the greatest common divisor of x and y. Solve Challenge. Any tips for improving this code and making it more efficient/faster would be appreciated. It >should also be noted that elements. 360 seconds in Python 2. NOTE: If you have forgotten your password, we are unable to help recover accounts if you have signed in at. A certain problem* states: For a positive integer n, let σ2(n) be the. 6. 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. For example, 3124 is one possible. brash • 12 yr. If you can solve. A permutation is an ordered arrangement of objects. 3x3 or 4x4 to show how the value should be computed. Runs for 1,409,343 iterations. g. For example, 3124 is one possible permutation of the digits 1, 2, 3 and 4. A unit fraction contains 1 in the numerator. 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. R","contentType":"file"},{"name. 4. If all of the permutations are listed numerically or alphabetically, we call it lexicographic order. 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. Problem 11. At the speed my code is currently running that will take like a billion years. 7 source. There exists exactly one Pythagorean triplet for which a + b + c = 1000. A number n is called deficient if the sum. Problem 24. permutations ( [x for x in range (0,10)], 10)) [999999] Using your brain way: We can sort of count permutations, we know the first permutation is 0123456789, and we know that for the first 9! permutations 0 will be the first digit, so when looking for. What is remarkable is that, by using the same digital substitutions, the anagram, RACE, also forms a square number: 9216 = 96^ (2). Title. 40GHz. The product of these numbers is 26 × 63 × 78 × 14 = 1788696. (Java Solution) Project Euler > Problem 176 > Right-angled triangles that share a cathetus. 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. First, generate four million pseudo-random numbers using a specific form of what is known as a "Lagged Fibonacci Generator": For 1 ≤ k ≤ 55. Multiples of 3 or 5. Three by three; 2. Clarifications on Project Euler Problems. Benchmark. Find the product abc. $endgroup$ – Paul Manta. 2 + 2 + 2 + 2 + 2. 980479. Project Euler challenges that I have done . Status. 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. ID. The lexicographic permutations of 0, 1 and 2 are. Project Euler is a series of coding challenges that have been popular for many years. diagonal_reverse (grid, run_len) ¶. The problem: —. Not really research, but I like to try the problems on Project Euler to reassure myself that I can still program. In addition you will find solutions from project euler problem sets. The raw processor instructions usually do FP division faster (e. 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. Benchmark. A permutation is an ordered arrangement of objects. If you have forgotten your username and/or password and you have generated an. Find the sum of all the multiples of 3. 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. (compiled for x86_64 / Linux, GCC flags: -O3 -march=native -fno-exceptions -fno-rtti -std=gnu++11 -DORIGINAL )My Algorithm. Benchmark. 40GHz. 02 seconds on an Intel® Core™ i7-2600K CPU @ 3. 23, 2023 — Training Time:. 11 seconds on an Intel® Core™ i7-2600K CPU @ 3. The correct solution to the original Project Euler problem was found in less than 0. It hosts a collection of around 600 different algorithm problems that get progressively harder, to the point where even people with math PhD's still struggle with them. current cell and its three neighbors going left and down. Find the largest palindrome made from the product of two n -digit numbers. The only point of interest is shift which is a power of 10 such that 10^a = shift leq x leq 10^ {a+1} 10a =shif t≤x≤10a+1. 1. More than 100 million people use GitHub to discover, fork, and contribute to over 420 million projects. Project Euler #5: Smallest multiple. append (the_word) return perm def perm (string): "Find all permutations of given string. Project Euler #8: Largest product in a series. 1. 01 seconds on an Intel® Core™ i7-2600K CPU @ 3. 01 seconds on an Intel® Core™ i7-2600K CPU @ 3. Title. Project Euler+ is a series of challenging mathematical and computational programming problems hosted on HackerRank. Each new term in the Fibonacci sequence is generated by adding the previous two terms. 1. ID. It is okay if you share just only the names of applicable formulas or theories. Peak memory usage was about 20 MByte. The correct solution to the original Project Euler problem was found in 0. 145 is a curious number, as 1! + 4! + 5! = 1 + 24 + 120 = 145. In this video I present some basic theorems on permutations and use them to solve Project Euler problem #24A challenge that will expand your computer science and math knowledge – all while giving you a ton of programming practice. NOTE: If you have forgotten your password, we are unable to help recover accounts if you have signed in at. 2. Question: PLEASE ANSWER IN JAVA. Euler Network's ongoing. The correct solution to the original Project Euler problem was found in 0. Consider the problem of building a wall out of 2×1 and 3×1 bricks (horizontal×vertical dimensions) such that, for extra strength, the gaps between horizontally-adjacent bricks never line up in consecutive layers, i. ; If F() is the counting function, then F(3,{3. Find the maximal run_len long product in the ‘reverse’ diagonal direction. In the United Kingdom the currency is made up of pound (£) and pence (p). Benchmark. I'm not looking to use a different method, I'm wondering why this code isn't working as is, from the debugging that I did it looks as everything that I am. Solved By. Status. Title. 40GHz. Most of the problems require parsing input of some kind. 40GHz. brash • 12 yr.