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Linear system of equations

Solve the system of equations in three variables.

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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)

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Sudoku square

We have a small Sudoku square, but one number is missing. x = [ 1 5 4 8 6 3 0 9 7 ] Make a function, wher...

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Solve the Sudoku Row

*Description* A simple yet tedious task occurs near the end of most Sudoku-solving algorithms, computerized or manual. The ta...

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What gear ratio does the cyclist need?

A cyclist (perhaps including our famed Codysolver the cyclist <http://www.mathworks.com/matlabcentral/cody/players/1841757-the...

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How Far Can You Throw Something?

As you probably learned in your high school physics class, throwing an object at a 45 degree angle will give you the maximum ran...

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center of mass

R is a given matrix with size [n,2]. R(i,:) is interpreted as the 2D-position of a mass point with mass i. Calculate the center ...

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Bernoulli's Equation

Bernoulli's equation states that for an incompressible fluid the following summation is constant across the flow: v^2/2 + g*z + ...

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Determine if a four bar mechanism is of Grashof type

A four bar mechanism is composed of four links. if s is the smallest link, l the longest and p,q are the length of the other lin...

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Mechanical Advantage of a Gear Train

Calculate the mechanical advantage of a gear train. The mechanical advantage of a gear couple is given by MA = T_o/T_i where ...

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Elastic Collision 001: 1-D

Elastic Collision of two particles. <http://en.wikipedia.org/wiki/Elastic_collision wiki Elastic Collision> Solve Conservat...

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Distance of the centroids of the balls

Given *n* balls of radius *r* and the vector *p (nx3)* with all position *(x,y,z)* of the balls, return the symmetric matrix *A ...

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Find the jerk

No, it's not the author of this problem... Jerk is the rate of change in acceleration over time of an object. So, if given t...

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Calculate compression ratio of engine

Calculate compression ratio of engine given compression volume of cylinder(Vc), piston stroke(s) and valve diameter(d)

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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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Center of mass

Given a matrix M(m,n), where m is the number of vertices of the geometrical element and n is 2 or 3 (2D-plane figure or 3D-solid...

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Energy of an object

Calculate the total mechanical energy of an object. Total Energy= Potential energy + Kinetic energy P.E.=m*g*h K.E.=1/2...

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Calculate the height of an object dropped from the sky

Assume that an object is dropped from 1000 meters above the surface of the earth at time t=0. The object is dropped such that t...

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Hangman (easy)

What is the best letter to start a <http://en.wikipedia.org/wiki/Hangman_(game) hangman> game with? You are given a cell arra...

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Pangrams!

A pangram, or holoalphabetic sentence, is a sentence using every letter of the alphabet at least once. Example: Input s ...

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Distance walked 1D

Suppose you go from position 7 to 10 to 6 to 4. Then you have walked 9 units of distance, since 7 to 10 is 3 units, 10 to 6 is 4...

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The Hitchhiker's Guide to MATLAB

Output logical "true" if the input is the answer to life, the universe and everything. Otherwise, output logical "false".

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Weighted average

Given two lists of numbers, determine the weighted average. Example [1 2 3] and [10 15 20] should result in 33.333...

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Rotate and display numbered tile

Imagine a square tile with four numbers on it, one on each edge. We will call these edges north, east, south, and west. If th...

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Find best placement for ordered dominoes (harder)

Given a list of ordered pairs, find the order they should be placed in a line, such that the sum of the absolute values of the d...

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Find perfect placement of non-rotating dominoes (easier)

Given a list of ordered pairs, find the order they should be placed in a line, such that the sum of the absolute values of the d...

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Golomb's self-describing sequence (based on Euler 341)

The Golomb's self-describing sequence {G(n)} is the only nondecreasing sequence of natural numbers such that n appears exactly G...

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Draw 'J'

Given n as input, generate a n-by-n matrix 'J' using 0 and 1 . Example: n=5 ans= [0 0 0 0 1 0 0 0 0 1 0 0 ...

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