Isaac

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Given a matrix, swap the 2nd & 3rd columns
If a = [1 2 3 4; 1 2 3 4; 1 2 3 4; 1 2 3 4]; then the result is ans = 1 3 2 4 1 3 2...

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Toeplitz Matrix
For a given square matrix of order n-by-n check whether this is a Toeplitz matrix or not. Return true if it is.

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ZigZag matrix with reflected format
ZigZag MATRIX with REFLECTED format. We have only input x. We have to create a matrix in the following pattern. input n=5...

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Sum of series VII
What is the sum of the following sequence: Σ(km^k)/(k+m)! for k=1...n for different n and m?

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Sum of series VI
What is the sum of the following sequence: Σk⋅k! for k=1...n for different n?

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Sum of series V
What is the sum of the following sequence: Σk(k+1) for k=1...n for different n?

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Sum of series IV
What is the sum of the following sequence: Σ(-1)^(k+1) (2k-1)^2 for k=1...n for different n?

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Sum of series III
What is the sum of the following sequence: Σ(2k-1)^3 for k=1...n for different n?

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Sum of series II
What is the sum of the following sequence: Σ(2k-1)^2 for k=1...n for different n?

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Approximation of Pi (vector inputs)
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...

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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 number of...

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Sum of series I
What is the sum of the following sequence: Σ(2k-1) for k=1...n for different n?

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Select every other element of a vector
Write a function which returns every other element of the vector passed in. That is, it returns the all odd-numbered elements, s...

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QWERTY coordinates
Given a lowercase letter or a digit as input, return the row where that letter appears on a standard U.S. QWERTY keyboard and it...

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Find relatively common elements in matrix rows
You want to find all elements that exist in greater than 50% of the rows in the matrix. For example, given A = 1 2 3 5 ...

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Finding Perfect Squares
Given a vector of numbers, return true if one of the numbers is a square of one of the numbers. Otherwise return false. Example...

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Interpolator
You have a two vectors, a and b. They are monotonic and the same length. Given a value, va, where va is between a(1) and a(end...

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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...

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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...

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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...

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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...

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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...

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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...

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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...

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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...

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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...

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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>> ...

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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>> ...

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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...

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Length of a short side
Calculate the length of the short side, a, of a right-angled triangle with hypotenuse of length c, and other short side of lengt...

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Isaac

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CUP Challenge Master

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