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Questions tagged [project-euler]

Project Euler is a series of challenging mathematical/computer programming problems. Please see the site and rules before posting.

0
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1answer
50 views

Formulae to find sum of all digits before n?

I've just started to learn algorithm by joining Project Euler, and trying to understand the below formula ...
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0answers
15 views

Extension of Gold for Pay problem

I've been struggling with an extension of the classical Gold for Pay question and was hoping to get some help with it. I was asked this in an online interview a couple days ago and could solve the ...
1
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1answer
59 views

What is going wrong with my solution for Project Euler 224?

I am trying to solve the HackerRank version. The problem statement, Let us call an integer sided triangle with sides a ≤ b ≤ c barely obtuse if the sides satisfy $a^2 + b^2 = c^2 - 1$. How ...
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1answer
25 views

Given $\sqrt {m^2+(n+o)^2}$ is int, is it possible that atleast one of $\sqrt {o^2+(n+m)^2}$ or $\sqrt {n^2+(o+m)^2}$ is also integer?

Given $m,n,o,\sqrt {m^2+(n+o)^2}\in\mathbb N$ and $o\le n\le m$, is it a guarantee that both of $\sqrt {o^2+(n+m)^2},\sqrt {n^2+(o+m)^2}$ are irrational? What I tried: Firstly, ${m^2+(n+o)^2}\le n^...
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217 views

Project Euler Problem #500

I need help solving Project Euler Problem #500 I was unable to find discussion on this topic. My approach to solve it is to use prime factorization of an unknown number, i.e. the answer, as $$x = 2^{...
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1answer
38 views

Walking positive square numbers and closing or opening doors [closed]

Peter moves in a hallway with $N+1$ doors consecutively numbered from $0$ through $N$. All doors are initially closed. Peter starts in front of door $0$, and repeatedly performs the following steps: ...
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0answers
71 views

Project Euler #119 how to get $a(x)$

Knowing that $512 = (5 + 1 + 2)^3$ (Sum of digits raised to certain power) and $614656 = (6+1+4+6+5+6)^4$ e.g: ex: $a(2) = 512$ ex: $a(10) = 614656$ ex: $a(70) = ...
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84 views

Combinatorics to calculate n choose k from set with repeated values.

Given a string of 48 characters, made out of 18 recurring characters, I am looking for the number of unique combinations of 1 to 15 character length strings one can make. Thus, I am looking for the ...
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1answer
49 views

Sum Equals Product: A Diophantine Equation

I formulated the following claim after reading Problem 88 of Project Euler: Fix $k$ and let $\mathscr N$ be the set of numbers $N$ satisfying $$N=n_1+n_2+\cdots+n_k=n_1n_2\cdots n_k,$$ where ...
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2answers
109 views

Finding integer solutions to $n^2 = 2d^2 - 2d + 1$

I'm trying to find the smallest integer solution to $$n^2 = 2d^2 - 2d + 1$$ Additional constraints: $$d > 10^{12}, n > 0$$ I wrote a computer program to bruteforce it, but that is too slow. ...
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2answers
223 views

Highly composite numbers and Abundant numbers

I'm working on Project Euler #23 and for the first time so far, I'm really confused, and the more I Google, the more confused I get. The problem states: A perfect number is a number for which the ...
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1answer
255 views

Project Euler 100 - can't understand solution

Problem I solved this using OEIS (finding smaller values and then searching OEIS for related sequences, it turned out that the exact sequence I needed was there) sequence. Looking at the thread, the ...
2
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1answer
107 views

Project Euler 9 - help understanding solution

I've been trying to understand the proof for a solution to the Euler 9 problem. I'm on this site under the heading "Solving the problem". I've understood the parts that came before it (excluding the "...
2
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1answer
144 views

Lattice paths - Project Euler

Problem 15 asks that how many routes there are through a $20×20$ grid(starting from upper left corner) only being able to move to the right and down. My answer is wrong. And i would like to know what ...
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2answers
284 views

Solving modified Fibonacci Nuggets [Project Euler 140]

I am trying to solve Modified Fibonacci golden nuggets. The generating function could be written as: $$A_G(x)=\frac{x(3x+1)}{1-x-x^2}$$ Let it be some $y\in\mathbb N$, then $$x(3x+1)=y(1-x-x^2)\\ x^...
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0answers
263 views

General summations of multiplicative functions

I have read about multiplicative functions. I also came across summations involving summation of multiplicative functions as well. Some summations were only over divisors of a number, which can be ...
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2answers
379 views

Combinatorics question based on ProjectEuler 606

Motivation The following text is from Problem 606 from Project Euler : A gozinta chain for $n$ is a sequence $\{1,a,b,...,n\}$ where each element properly divides the next. For example, there ...
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3answers
562 views

Amount of numbers not divisible by 7 in Pascals Triangle without iteration

For project Euler 148 problem, I want to get the amount of numbers in Pascals Triangle that are not divisible by 7 in row 0 to n where n is $10^9$. Find the number of entries which are not ...
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2answers
635 views

project euler #577 confusion

Problem Link. An equilateral triangle with integer side length $n≥3$ is divided into $n^2$ equilateral triangles with side length 1 as shown in the diagram in the above link. The vertices of these ...
3
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1answer
451 views

Modeling path of a rolling ellipse

I'm trying to solve Project Euler problem 525. My approach is to find a parametric equation that can model the path of the center point as it rolls, then take the arc length of that function for one ...
2
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3answers
176 views

How to evaluate closed form of these series of sum? $\sum_{k=1}^n k*10^{k-1}$

$$\sum_{k=1}^n k*10^{k-1}$$ I came across this summation of series while I was trying to solve Project Euler Problem 40. The problem can be solved without using this method; however, I want to know ...
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2answers
434 views

How to compute quintinomial coefficients?

I'm looking for a way to compute elements of a quintinomial triangle. Is there a general case? To be more specific I'm looking for a way to compute the coefficients of the polynomial $(x^4 + x^3 + x^...
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1answer
149 views

Stirling numbers and bernoulli numbers for summing up n numbers to the kth power

I am currently working on problem 487 on project euler. I did some research and I only see 2 possibilities to solve this problem: 1. By using faulhabers formula 2. by using the formula featuring the ...
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2answers
198 views

How many digits of accuracy will an answer have?

I was doing a project Euler problem where I needed to find several Fibonacci numbers, but their index was so large that I could not use the typical recursive method. Instead, I used Binet's rule: $$ ...
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0answers
81 views

Divisor antichain related algorithm

I have thought about problem 386 for 2 months and I have given up. A divisor antichain of a number is a subset of its (positive) divisors no one of which is divisible by another (e.g. for $30$ $(2,3,5)...
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1answer
167 views

Order statistics of scaled beta distributions (Project Euler 573)

I am trying to solve Project Euler problem 573. To summarize my understanding of the problem: in a race with $n$ contenders, runner $k$ runs at speed $v_{k} = k/n$ and has to cover the distance $D_k ...
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0answers
98 views

Number of distinct values for $a^b$ with $2 \leq a \leq 100$ and $2 \leq b \leq 100$

This is the 29th Project Euler problem. I've been going crazy trying to spot where I've made a mistake. My thinking is to first assume that there are no duplicate values, i.e. all 99 values of $a$ ...
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2answers
443 views

Project Euler problem #3 (how to do it by hand?)

Problem #3 in Project Euler: What is the largest prime factor of the number $600851475143$? I want to solve this by hand. (I am doing this with all problems.) What techniques would allow me to ...
2
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1answer
488 views

How did I mix up this expected value problem (Project Euler 151)?

I'm working on project Euler 151 which goes as follows: A printing shop runs 16 batches (jobs) every week and each batch requires a sheet of special colour-proofing paper of size A5. Every ...
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2answers
984 views

Parametrization of Cardano triplet

I'm solving project euler problem 251. I arrived at the conclusion that $$\sqrt[3]{a+b\sqrt{c}}+ \sqrt[3]{a-b\sqrt{c}}=1 $$ can be written as $$8a^3+15a^2+6a-27b^2c=1$$ That is really faster to ...
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0answers
791 views

Project Euler's, Problem #565

Project Euler's, Problem #565 states: Let $\sigma(n)$ be the sum of the divisors of $n$. E.g. the divisors of $4$ are $1, 2$ and $4$, so $\sigma(4)=7$. The numbers $n$ not exceeding $20$ ...
3
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1answer
86 views

How many sets correspond to connected graphs

I'm trying to solve this project euler problem. I don't want to get too much help, since that would defeat the purpose, but I'm hitting a wall, so I'm asking a related problem here, from which I'll ...
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2answers
114 views

Possible mis-interpretation in Project Euler #21

Here is the problem statement for Problem 21 of Project Euler. Let $d(n)$ be defined as the sum of proper divisors of $n$ (numbers less than $n$ which divide evenly into $n$). If $d(a) = b$ ...
2
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1answer
3k views

The largest product of two n-digit numbers which is palindrome

Project Euler: 4 is stated as follows: Largest palindrome product A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 =...
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0answers
210 views

Game of Nim: Losing Positions [closed]

If you have heard of the game Nim, this is a version of the game. However, in this version, the players can only remove the amount of stones from the pile which is coprime to the current pile size. ...
4
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1answer
606 views

The 9 most significant digits in Fibonacci series (Project Euler 104)

With regards to project Euler, problem 104: https://projecteuler.net/problem=104 The essence of the question here is how to keep track of the 9 most significant digits of a Fibonacci series (Keeping ...
2
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1answer
238 views

Project Euler 106: Necessary and sufficient conditions

Problem Statement Let S(A) represent the sum of elements in set A of size n. We shall call it a special sum set if for any two non-empty disjoint subsets, B and C, the following properties are true:...
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2answers
147 views

Proof that nonconstant polynomial cannot have the same value at all integer points

I am reading the solution to the Project Euler problem 28 here, specifically the one under 'Deriving a non-iterative formula'. That solution first deduces the degree of the polynomial, and then ...
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2answers
168 views

(Soft Question) Is it bad to use Sage built in functions instead of creating my own?

I've been doing Project-Euler just as a way to increase my competency in computer science. I'm currently a Pure and Applied Math major who recently adopted computer science as a minor in order to ...
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0answers
230 views

How to simplify a sum of complex divisors?

This question arises from Project Euler 153. That problem asks for the sum of all complex divisors of all natural numbers up to a maximum, where a complex divisor is a complex number of the form a + ...
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1answer
2k views

Project Euler, Problem #529 10-substrings

Have anyone tried the problem 529? I tried but I'm confronted to a very high complexity $O(N^2)$ with $N$ being the length of the number. The code is: ...
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1answer
67 views

Statement from explanation of “What is the smallest number divisible by each of the numbers 1 to 20?” on Project Euler

Here is part of explanation from the PE problem 5: Let us consider the case of finding the least value of $N$ for $k=20$. We know that $N$ must be divisible by each of the primes, $p[i]$, less than ...
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2answers
837 views

Expected value of a guessing game

I'm trying to solve project euler 527, I don't understand how the expected value of B(6) is taken. A secret integer t is selected at random within the range 1 ≤ t ≤ n. The goal is to guess the ...
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2answers
257 views

Explaining solution of Project Euler problem #5

Here is the problem. Pretty simple to brute force, but more gently solutions are not that easy to understand, and I'm not talking about programming issue, but math-affiliated. For example, I'm ...
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0answers
144 views

About an answer given for Project Euler 19

The problem is here and someone gave this answer but I don't understand it even if I know the rule of large numbers. If you want to write a code for this, it is really boring. On the other hand, if ...
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0answers
531 views

Project Euler Problem #87 - Prime power triples

I found this problem in Project Euler: https://projecteuler.net/problem=87 The smallest number expressible as the sum of a prime square, prime cube, and prime fourth power is $28$. In fact, there ...
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1answer
159 views

Finding the last nonzero digit of the factorial of a large number

This problem is from projecteuler problem 160. I am not looking for an answer or anything like that I just got stuck on some of the mathematics and am looking for some help. Instead of solving the ...
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1answer
174 views

Summation of a function

Let $n$ is a positive integer. $n = p_1^{e_1}p_2^{e_2}...p_k^{e_k}$ is the complete prime factorization of $n$. Let me define a function $f(n)$ $f(n) = p_1^{c_1}p_2^{c_2}...p_k^{c_k}$ where $c_k = ...
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2answers
637 views

square of digits - why does it always contain 1 or 89 [closed]

I attempted project euler problem 92, while I passed it, my solution works, but had just...awful performance. So I would like to try again tomorrow. In the meantime understanding why the iteration ...
0
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1answer
131 views

Where is my formula false??

I wrote a formula that returned how many numbers in a given row of pascals triangle are divisible by a given prime. This formula was created to answer https://projecteuler.net/problem=148. I was ...