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Matrix Pattern 1

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Chess ELO rating system
The Elo rating system is a method for calculating the relative chess skill levels of players in competitor-versus-competitor gam...

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Wheat on a chessboard pt 2
If a chessboard were to have wheat placed upon each square such that x grains were placed on the first square and each successiv...

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Wheat on a chessboard pt 1
If a chessboard were to have wheat placed upon each square such that one grain were placed on the first square and each successi...

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Generate a point cloud on an equilateral triangle 1
The input is the iteration parameter H. The output is a point cloud W involving N points. W is N uniformly distributed points ...

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Counting in Finnish
Sort a vector of single digit whole numbers alphabetically by their name, in Finnish. See the Wikipedia page for <http://en.wik...

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Find the Area of a Polygon
Consider 2-D geometry and assume that the points are given in form of rows of a matrix. Find the area of polygon enclosed by the...

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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=12 and h=4, the result is [0.8 0.8 ...

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Plotting Practice
Plot cos(x) vs x as shown in the figure below. Include the appropriate title, x-label, and y-label. Note, it is case sensitive. ...

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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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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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LED Current Calculation
In an electrical circuit, the current (III) flowing through an LED is determined using Ohm’s Law: Where: I is the current ...

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Estimating Monthly Electricity Cost for a Household Appliance
You recently bought an electric kettle for your kitchen, and you want to estimate how much it costs to run every month. The kett...

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Voltage Divider Calculation
A voltage divider is a simple circuit used to obtain a reduced voltage from a higher voltage source using two resistors in serie...

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Inductor Energy Storage Calculation
The energy (EEE) stored in an inductor is given by the formula: Where: E is the energy in joules (J) L is the inductance in...

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Calculate Charge Using Capacitance and Voltage
The charge (Q) stored in a capacitor is given by the formula:Q=C×V where: C is the capacitance (in farads) V is the voltage (...

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Energy Stored in a Capacitor
The energy (E) stored in a capacitor is given by the formula: where: C is the capacitance (in farads) V is the voltage (in ...

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Calculate Current in a Series Circuit Using KVL
Kirchhoff's Voltage Law (KVL) states that the sum of voltages around a closed loop is zero. Given a voltage source (V) and three...

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Calculating the Total Resistance in a Series Circuit
Description: In a series circuit, the total resistance is the sum of the individual resistances. This problem asks you to write ...

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Simple Electrical Power Calculation
Calculate the electrical power using the formula: P=V×I where: V is the voltage (in volts) I is the current (in amperes)

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Ohm’s Law - Calculate Resistance
Ohm’s Law states that resistance R can be calculated as:R=V/I where: V is the voltage (in volts) I is the current (in ampere...

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Spiral Mandala
Generate a clockwise spiral pattern using 1s in an N×N matrix to create an intricate mandala effect. e.g. N = 5; y_correct...

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Concentric Squares Mandala
Generate concentric square rings of alternating 1s and 0s to form a layered mandala-style matrix. e.g. N = 5; 1 1 1 1 1;...

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Starburst Mandala
Create a mandala starburst using diagonal and orthogonal symmetry in a matrix.

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Hourglass Mandala
Generate an hourglass shape using matrix geometry and symmetry. e.g. N = 5; 1 1 1 1 1; 0 1 1 1 0; ...

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Vertical Mirror Mandala
Create a symmetric left-right mirrored pattern in an N×N matrix to emulate mandala reflection symmetry. e.g. N = 5; ...

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Plus Cross Mandala
Create a symmetrical plus (+) shaped pattern centered in an N×N matrix.

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Diagonal Cross Mandala
Generate an N×N matrix with diagonals highlighted to form an artistic X-shaped mandala pattern. e.g. N = 5; 1 0 0...

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Circular Ring Approximation Mandala
Generate a matrix that approximates a circular ring using distance-based thresholding , a visually rich mandala-inspired challen...

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Hollow Diamond Pattern
Create an N×N matrix that forms a hollow diamond shape using 1s, leaving the interior empty. This challenge emphasizes boundary ...

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