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The Ulam Matrix
The Ulam spiral is simple to describe. On a gridded piece of paper, write down the number 1. Then write successive integers as y...

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Determine if input is a perfect number
A <http://en.wikipedia.org/wiki/Perfect_number/ perfect number> occurs whent the sum of all divisors of a positive integer, exce...

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Sum the Digits of a Number
Given an integer, sum the digits repeatedly until you end up with a single value less than 10. For example, if you add the di...

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Response of First Order Control Systems
In practice, the input signal to an automatic control system is not known ahead of time but usually random in nature. Thus, in t...

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Separate even from odd numbers in a vector - without loops
*Without using loops*, rearrange a vector of integers such that the odd numbers appear at the beginning, and even numbers at the...

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Find Month & day for given day number of a year
Find Month & day for given day number of a year (day number is any number ranging from 1 to 366)

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Determine if input is a valid AHP evaluation matrix
Input is a matrix. Output is a true or false statement (1 or 0). Return true if input is a valid Analytic Hierarchy Process eval...

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Vectorize the digits of an Integer
Create a vector of length N for an integer of N digits. x = 123045; x_vec = [1 2 3 0 4 5]; I happened upon a trick ...

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Remove all the consonants
Remove all the consonants in the given phrase. Example: Input s1 = 'Jack and Jill went up the hill'; Output s2 is 'a ...

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Remove the vowels
Remove all the vowels in the given phrase. Example: Input s1 = 'Jack and Jill went up the hill' Output s2 is 'Jck nd Jll wn...

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is the number happy?
test is a given integer number is Happy of not? answer 1 if yes or 0 is no

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Dudeney Numbers: Numbers which are the cube of their decimal sum
From Wikipedia: _A Dudeney number is a positive integer that is a perfect cube such that the sum of its decimal digits is equa...

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Factorions: Numbers that equal the sum of the factorials of their digits
From Wikipedia: _A factorion is a natural number that equals the sum of the factorials of its decimal digits_ For example: ...

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Matrix Pattern 9

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Find the sines of an isosceles triangle when given its area and height
Find the sines of an isosceles triangle when given its area and height. For example, when A=60 and h=5, the result is [0.3752...

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Max Change in Consecutive Elements
If an array is given as input then find the index of consecutive elements that represent maximum change. Example: Input ...

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Matrix Pattern 8

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SatCom #1: Wavelength of an electomagnetic wave
*Satellite and Space Engineering - Problem #1* _This is the first of a series of problems looking at topics in satellite and ...

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Calculate quadrilateral Area: sides and diagonals given

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Make an identity matrix whose diagonal elements are 1:n
For a given input n, make an n by n identity matrix that contains the elements 1:n along its diagonal. For example, if input=5: ...

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Reepeating numbers in array
Repeating numbers in array In = [1 0 0 0 2 0 0 0 3 0 0 0 0 0 5 0 0 0 0]. Out = [1 1 1 1 2 2 2 2 3 3 3 3 3 3 5 5 5 5 5].

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How unique?
Sometimes, when we check unique entries of vector we would like to know how many times each value occurs. Given vector of num...

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Largest territory
Determine whose territory is largest. If there are multiple numbers tied for the largest territory, return the smallest number. ...

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Kepler's Equation
Solve <http://en.wikipedia.org/wiki/Kepler's_equation Kepler's Equation>. Note that the solution is rounded down to 5 decima...

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Replace pattern 0 1 0 and 1 0 1
Find and replace a pattern in a row of zeroes and ones. * Find 1 0 1 and replace it with 1 1 1 * Find 0 1 0 and replace it w...

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Time Expansion
How can you slow down any discrete-time signal? Example Input original signal x. x = [1 2 3 -1 -2 -5 -4] We want t...

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Matrix indexing with two vectors of indices
Given a matrix M and two index vectors a and b, return a row vector x where x(i) = M(a(i),b(i)).

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Reindex a vector
You are given two vectors of equal length. Vector N has numeric values (no Inf or NaN) while vector IDX has integers. Place th...

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D'Hondt Method of Proportional-Representation
The D'Hondt method is a proportional representational method for allocating seats to parties in an election. <https://en.wiki...

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