# Ruizhe Gu

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Solved

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 ...

3 months ago

Solved

Project Euler: Problem 10, Sum of Primes

The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17. Find the sum of all the primes below the input, N. Thank you <http:/...

3 months ago

Solved

Project Euler: Problem 9, Pythagorean numbers

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 =...

3 months ago

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Project Euler: Problem 8, Find largest product in a large string of numbers

Find the greatest product of five consecutive digits in an n-digit number. 73167176531330624919225119674426574742355349194934...

3 months ago

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Project Euler: Problem 7, Nth prime

By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13. What is the Nth prime nu...

3 months ago

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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 ...

3 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...

3 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...

3 months ago

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Project Euler: Problem 2, Sum of even Fibonacci

Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 te...

3 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...

3 months ago

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Solve a System of Linear Equations

*Example*: If a system of linear equations in _x₁_ and _x₂_ is: 2 _x₁_ + _x₂_ = 2 _x₁...

3 months ago

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Verify Law of Large Numbers

If a large number of fair N-sided dice are rolled, the average of the simulated rolls is likely to be close to the mean of 1,2,....

3 months ago

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Find the Oldest Person in a Room

Given two input vectors: * |name| - user last names * |age| - corresponding age of the person Return the name of the ol...

3 months ago

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Convert from Fahrenheit to Celsius

Given an input vector |F| containing temperature values in Fahrenheit, return an output vector |C| that contains the values in C...

3 months ago

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Calculate Amount of Cake Frosting

Given two input variables |r| and |h|, which stand for the radius and height of a cake, calculate the surface area of the cake y...

3 months ago

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Dimensions of a rectangle

The longer side of a rectangle is three times the length of the shorter side. If the length of the diagonal is x, find the width...

3 months ago

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Area of an Isoceles Triangle

An isosceles triangle has equal sides of length x and a base of length y. Find the area, A, of the triangle. <<https://imgur...

3 months ago

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Is this triangle right-angled?

Given three positive numbers a, b, c, where c is the largest number, return *true* if the triangle with sides a, b and c is righ...

3 months ago

Solved

Find a Pythagorean triple

Given four different positive numbers, a, b, c and d, provided in increasing order: a < b < c < d, find if any three of them com...

3 months ago

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Is this triangle right-angled?

Given any three positive numbers a, b, c, return true if the triangle with sides a, b and c is right-angled. Otherwise, return f...

3 months ago

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Triangle sequence

A sequence of triangles is constructed in the following way: 1) the first triangle is Pythagoras' 3-4-5 triangle 2) the s...

3 months ago

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Length of the hypotenuse

Given short sides of lengths a and b, calculate the length c of the hypotenuse of the right-angled triangle. <<https://i.imgu...

3 months ago

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Area of an equilateral triangle

Calculate the area of an equilateral triangle of side x. <<https://i.imgur.com/jlZDHhq.png>> Image courtesy of <http://up...

3 months ago

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Side of a rhombus

If a rhombus has diagonals of length x and x+1, then what is the length of its side, y? <<https://imgur.com/x6hT6mm.png>> ...

3 months ago

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Side of an equilateral triangle

If an equilateral triangle has area A, then what is the length of each of its sides, x? <<https://i.imgur.com/jlZDHhq.png>> ...

3 months ago

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System of equations

Find a solution to a system of equations represented by a |n| by |n+1| matrix. For instance, [ 2 0 4; => 2*x = 4 ...

3 months ago

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Is this matrix orthogonal?

Given a square matrix, a, determine whether it is orthogonal. INPUT: a, a n x n matrix OUTPUT: true or false

3 months ago

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Solve the set of simultaneous linear equations

Given this pair of simultaneous linear equations: 2x + 3y = 23 3x + 4y = 32 Find the solution set (x,y)

3 months ago

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Plot Damped Sinusoid

Given two vectors |t| and |y|, make a plot containing a blue ( |b| ) dashed ( |--| ) line of |y| versus |t|. Mark the minimum...

3 months ago

Solved

Column norms of a matrix

Given a matrix M, return a vector y such that for each k y(k)=norm(M(:,k)) (y(k) is the Euclidean norm of the k-th col...

3 months ago