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Project Euler: Problem 6, Natural numbers, squares and sums.

The sum of the squares of the first ten natural numbers is, 1^2 + 2^2 + ... + 10^2 = 385 The square of the sum of the first ...

9 months ago

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Project Euler: Problem 5, Smallest multiple

2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder. What is the smalle...

9 months ago

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Project Euler: Problem 4, Palindromic numbers

A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 ...

9 months ago

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Project Euler: Problem 1, Multiples of 3 and 5

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...

9 months ago

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Generalised Hamming Number

Inspired by Project Euler n°204 and Problem 1308 by James A generalised Hamming number of type n, has no prime factor larger ...

9 months ago

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Perimeter of a semicircle

Given the diameter d, find the perimeter of a semicircle

9 months ago

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Given a square and a circle, please decide whether the square covers more area.

You know the side of a square and the diameter of a circle, please decide whether the square covers more area.

9 months ago

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Approximation of Pi

Pi (divided by 4) can be approximated by the following infinite series: pi/4 = 1 - 1/3 + 1/5 - 1/7 + ... For a given numbe...

9 months ago

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Pi Digit Probability

Assume that the next digit of pi constant is determined by the historical digit distribution. What is the probability of next di...

9 months ago

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radius of a spherical planet

You just measured its surface area, that is the input.

9 months ago

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Pi Estimate 1

Estimate Pi as described in the following link: <http://www.people.virginia.edu/~teh1m/cody/Pi_estimation1.pdf>

9 months ago

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Calculate area of sector

A=function(r,seta) r is radius of sector, seta is angle of sector, and A is its area. Area of sector A is defined as 0.5*(r^2...

9 months ago

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Pizza!

Given a circular pizza with radius _z_ and thickness _a_, return the pizza's volume. [ _z_ is first input argument.] Non-scor...

9 months ago

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Get all prime factors

List the prime factors for the input number, in decreasing order. List each factor. If the prime factor occurs twice, list it as...

9 months ago

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Factorize THIS, buddy

List the prime factors for the input number, in decreasing order. List each factor only once, even if the factorization includes...

9 months ago

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Numbers with prime factors 2, 3 and 5.

Make a function which takes one positive integer n and returns a matrix with the numbers of the form (2^i)*(3^j)*(5^k) which are...

9 months ago

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Find vampire numbers

A <http://en.wikipedia.org/wiki/Vampire_number vampire number> is a number v that is the product of two numbers x and y such th...

9 months ago

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Proper Factors

Generate the proper factors of input integer x and return them in ascending order. For more information on proper factors, refer...

9 months ago

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Multiples of a Number in a Given Range

Given an integer factor _f_ and a range defined by _xlow_ and _xhigh_ inclusive, return a vector of the multiples of _f_ that fa...

9 months ago

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Project Euler: Problem 3, Largest prime factor

The prime factors of 13195 are 5, 7, 13 and 29. What is the largest prime factor of the number being input, input might be ui...

9 months ago

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Smith numbers

Return true if the input is a Smith number in base ten. Otherwise, return false. Read about Smith numbers at <http://en.wikipedi...

9 months ago

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Prime factor digits

Consider the following number system. Calculate the prime factorization for each number n, then represent the prime factors in a...

9 months ago

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Find an optimal placement of coolers on a grid

In a certain chemical plant, 6 new pieces of cooling equipment (coolers) are to be installed in a vacant space. This vacant spac...

9 months ago

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Calculate the sphericity of a Raschig ring

Sphericity is a measure of the roundness of any particle. It was defined by Wadell in 1935 as the ratio of the 'surface area of ...

9 months ago

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Characterize fluid flow in a pipe as to laminar or turbulent

In fluid mechanics, characterizing the flow in a pipe is essential to predicting its behavior. The flow pattern can either be la...

9 months ago

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Compute the missing quantity among P, V, T for an ideal gas

Consider 100 mol of helium gas at a certain pressure (P), volume (V), and temperature (T). Assuming that the ideal gas law appli...

9 months ago

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Find an overlap in the cleaning schedule of two tank reactors

In a certain pharmaceutical production company, there are two tank reactors operating simultaneously and independent of each oth...

9 months ago

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Assess the scatter of wind turbines in a field

The renewable energy industry is on the rise in many countries--- and one of the key players is wind energy. It is believed ...

9 months ago