# Tagged Questions

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

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### Combinations/Permutations Count Paths Through Grid

I am curious about a situation in permutations/combinations. This question stems from a challenge site (project euler, problem 15) and research found on this exchange and elsewhere. The question ...
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### Project Euler Question 222

Would I be wrong to assume that the solution to this problem: What is the length of the shortest pipe, of internal radius 50mm, that can fully contain 21 balls of radii 30mm, 31mm, ..., 50mm? ......
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### Generating Numeric Palindromes.

I have just started the Euler project, and felt like I didn't get the fourth problem right...I used string conversion to test if my numbers were symmetrical, instead of relying on (the much faster) ...
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### Comparing powers without logarithms

Related to this question and this Project Euler problem (Problem 99), I came up with a recursive algorithm for comparing two numbers of the form $x^y$ (with $x>1$ and $y\ge 0$) without explicit use ...
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### Bell-like recurrence

Let $$A(n)=\sum_{k=0}^{n-1}\binom{n}{k}A(k)+n!,\quad A(0)=1$$ $$B(n)=\sum_{k=0}^{n-1}\binom{n}{k}B(k)-n!-n!\sum_{k=1}^{n}\frac{1}{k!},\quad B(0)=-1.$$ I'm interested in computing $S(n)=A(n)+B(n)$ ...
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### What is the max possible value of the sum of power of y of each digits?

I'm trying to solve the 30th euler problem. My code is working, but I'm not sure if it's luck or ingeniousness. To be the most efficient, I want to reduce at the maximum the numbers to checks. I ...
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### What is wrong with my algorithm (finding if the origin is within a triangle's interior)?

I am working on Project Euler Problem 102 and I thought I had a solution, but it seems I do not. Now, don't give me the solution. I know I'm on the right track. What I want to know is why my method ...
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### Computing Non-zero End Digits of Large Factorials

Any large factorial will have a number of zero behind it, and one could write an expression to compute the number of trailing zeros, but how would one go about computing the non-zero end digits? E.g. ...
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### Project Euler 215 - Solving with Sparse Matrices and Vector Multiplication

I wrote a program to solve Project Euler Problem #215 (see below for description) using memoization, and when I got access to the PE forums, I saw everyone else wrote programs that also used dynamic ...
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### How is this probability found (project euler #121)?

In the problem statement of project Euler problem 121, the following information is given: A pouch contains one black chip and one white chip. In a simple game, one player takes a chip at random and ...
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### Project Euler Problem 338

I'm stuck on Project Euler problem 338. This is a cross post from StackOverflow where I initially posted, however, it was suggested that I post it here too since the problem mostly relies on math. The ...
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### Project Euler, Problem #25

Problem #25 from Project Euler asks: What is the first term in the Fibonacci sequence to contain 1000 digits? The brute force way of solving this is by simply telling the computer to generate ...
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### How many routes are there through from top left corner to top right in a 20x20 grid? Binomial Coefficent explanation [duplicate]

Possible Duplicate: Counting number of moves on a grid I'm trying to solve this computer programming problem on Project Euler: http://projecteuler.net/index.php?section=problems&id=15 ...
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### Project Euler analyzing and simplifying problem 33

These questions concern "Project Euler problem 33": The fraction $\displaystyle \frac {49}{98}$ is a curious fraction, as an inexperienced mathematician in attempting to simplify it may ...
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### Number of closed paths formed by arcs of one fifth of a circle

**I was trying to solve the following issue: Find the number of possible closed paths using one fifth of an arc ($72^o$), where at each time step we can move either clockwise or anti-clockwise. in ...
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### Need a nudge in the right direction - How do I find the total number of permutation with 3 consecutive characters?

Again, I really just want a nudge in the right direction. Possibly a large nudge, but not the straight forward answer. I am trying to figure out how to solve Project Euler Problem 191. I believe I ...
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### Primitive integer triangles

Consider the triangles with integer sides $a$, $b$ and $c$ with $a \leq b \leq c$. An integer sided triangle $(a,b,c)$ is called primitive if $gcd(a,b,c)=1$. How many primitive integer sided triangles ...
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### Combinatorial counting

This question is about Project Euler 113: Working from left-to-right if no digit is exceeded by the digit to its left it is called an increasing number; for example, 134468. Similarly ...
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### Find the sum of all the multiples of 3 or 5 below 1000

How to solve this problem, I can not figure it out: If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23. Find the sum of ...
On a two dimensional plane, line $X$ is at an angle of $x$ radians and an incoming light travels at an angle of $y$ radians. How can I calculate the angle of the outgoing light reflected off of the ...
This is in relation to the Euler Problem $13$ from http://www.ProjectEuler.net. Work out the first ten digits of the sum of the following one-hundred $50$-digit numbers. \$...