# Questions tagged [project-euler]

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

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### Is there a way to find an upper bound for $n^2+an+b$?

I was solving the Project Euler: Problem 27. Considering quadratics of the form $n^2 + an + b$, where $|a| \lt 1000$ and $|b| \le 1000$ Find the product of the coefficients, $a$ and $b$, for the ...
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### Project Euler #329 (Prime Frog) - Stochastic independence

Susan has a prime frog.Her frog is jumping around over 500 squares numbered 1 to 500. He can only jump one square to the left or to the right, with equal probability, and he cannot jump outside the ...
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### Why is the one quadratic polynomial a perfect square more often than the other?

I was solving problem 137 of Project Euler, which led me to find $n$ such that $5n^2+2n+1$ is a perfect square. But such numbers are very rare (the 13th is around 3 billions) so after decomposing into ...
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### Is there a way to find a bound on the largest prime factor a given number n?

I worked on Project Euler problem 3 (find largest prime factor of 600851475143) a while back and have tweaked with the code a few times to reuse for other problems, but I eventually found that there ...
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### Spider Fly Problem

I am trying to solve Project Euler problem 86. I know I have to generate Pythagorean triplets and so on. But I have a problem with choosing valid cuboids. For example if the dimensions of the cuboid ...
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### How to solve for var r in closed-form arithmetic-geometric function? (Euler problem 235)

Disclaimer: Math noob here. I have this arithmetic-geometric sequence $u(k)=(a-dk)r^{k-1}$ and summation $s(n)=\sum_{k=1}^n u(k)$ Using Wikipedia (sources 1, 2, and 3), I have solved for the closed-...
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### How does a < b < c and a + b + c = s imply a < s/3 and b < s/2?

I've been trying to understand the overview given for problem 9 on Project Euler and it mentions that the upper bound for iterating through possible values of a is (s - 3)/3 and for b it is (s - a)/2. ...
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### 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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### 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 divisible ...
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### 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 ...
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### 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 ...
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### 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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### 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 ...