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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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Generate Square Wave
Generate a square wave of desired length, number of complete cycles and duty cycle. Here, duty cycle is defined as the fraction ...

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Smallest distance between a point and a rectangle
Given two points *x* and *y* placed at opposite corners of a rectangle, find the minimal euclidean distance between another poin...

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Great Circle Distance
Find shortest between two points on a ball given their azimuthal and polar angles (in degrees) as well as the radius of the sphe...

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Clockwise or Counterclockwise
Given a list of 2-d points defining the vertices of a polygon, determine whether these points are sorted clockwise. The input...

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Breaking Out of the Matrix
Do you want to take the Red Pill, or the Blue Pill? If you take the Blue Pill, you will simply pass along to the next problem...

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TRON strategy toggle
Detect whether your lightcycle is on same side of existing walls as opponents lightcycle. This function is useful in toggling a ...

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Detect circles in images
Given an image and a target radius range, specified as [rmin rmax], find circles in the image. Your function should output an m-...

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Index of neighbor pixel with steepest gradient
Unlike in various applications, where the gradient of a two dimensional matrix is calculated in x and y direction, the gradient ...

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Compute the dilation of a binary image
A basic operation in image analysis is the dilation. Given an image where each pixel is either on or off (black/white, true/fals...

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2D - Mean Filter
Assume you are given an "image" matrix of size NxM. Reduce the image noise by implementing a mean filter window of size 9 (a 3x3...

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Create an 8-color version of an image
This problem was inspired by a tweet I saw from @MATLAB regarding <http://www.mathworks.com/matlabcentral/fileexchange/37816-the...

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Create different color vectors.
When producing figures with multiple lines on, you often want the lines to all be visible and different colors. Given the need f...

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Make blocks of color
Given a (Nx3) sequence of RGB colors, I want to create a (numRowBlocks x numColBlocks x 3) image comprising (blockSize x blockSi...

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Change a specific color in an image
The ability to change colors can be a useful tool in image processing. Given an m x n x 3 array (much like CData in images), fin...

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Dog Statistics
The vectors ht and wt contains the heights and weights of 20 golden retrievers. In some cases, it was not possible to make both ...

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Simpson's Paradox - Calculate correlation coefficients for groups of data
Simpson's Paradox is a statistical phenomenon where groups of data can have a characteristic while the whole data set together h...

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Orthonormal matrix
You decide whether any given matrix is an orthonormal matrix or not. If each column in a matrix is perpendicular to the other...

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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 ...

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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...

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Design a tubesheet for shell-and-tube heat exchangers
<<https://3.bp.blogspot.com/-kLSbhcCoT2I/WJIh-QVGLGI/AAAAAAAADEs/svvMzBqn4fUfI1rTCCH7Uw-QuDvxx0PxACLcB/s1600/Screenshot_669.jpg>...

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Count the number of folds needed to pack a large sheet
In a certain paper factory, large sheets of paper are being made every day. Before sending the sheets for shipment, they have to...

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Create a matrix map of increasing safety levels
The sole nuclear power plant at Grid City suddenly had a meltdown. Luckily, the plant was designed to be in full automation, so ...

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Convert a temperature reading from Celsius to an unknown scale
Two of the most famous temperature scales are the Celsius and the Fahrenheit scale. In reality, however, there are so many other...

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Expand 10^n to Powers of 4
Given an integer n, return the coefficients c = [c_n,c_n-1,...,c_0] Such that 10^n = c_n*4^(n) + c_n-1*4^(n-1...

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Math with Roman Numerals
Given a function R within (+,-,*,/) and two Roman numerals a & b, compute aRb in Roman numerals.

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Split bread like the Pharaohs - Egyptian fractions and greedy algorithm
How would you split 5 loaves of bread among 8 people in all fairness? Get a hint from the Pharaohs. 5/8 = 4/8 + 1/8 , i.e. each ...

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Converting numbers back from extended form
Thanks for all the help you guys gave me on writing out the numbers in extended form in <http://www.mathworks.com/matlabcentral/...

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Numbers in extended form
Shhhhhhh. Don't tell my daddy, but I'm borrowing his Cody account so all of you very smart people can help me out. I just star...

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Additive persistence
Inspired by Problem 2008 created by Ziko. In mathematics, the persistence of a number is the *number of times* one must apply...

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