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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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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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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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Filled Diamond Pattern
Create an N×N binary matrix that forms a filled diamond shape centered in the matrix. The diamond expands symmetrically toward t...

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Compute the Tetris sequence
In the Tetris sequence, which starts with a 1, the next term is the smallest positive integer not already in the sequence that h...

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Simulate full-stop emergency braking scenario.
Emergency braking events demand rapid deceleration to bring the vehicle safely to rest. Given initial vehicle speed and constant...

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Compute optimal regenerative and friction brake torque blending.
Electric and hybrid vehicles combine regenerative braking with traditional friction braking to maximize energy recovery while en...

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Estimate brake disc temperature rise during braking.
During braking, kinetic energy is converted into thermal energy, causing brake discs to heat up. Excessive temperature rise can ...

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Compute optimal front–rear brake force distribution.
Modern braking systems dynamically distribute braking forces between front and rear axles to maintain stability, reduce stopping...

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Compute wheel slip ratio during braking.
During braking, a difference develops between the vehicle’s forward speed and the rotational speed of its wheels. This differenc...

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Estimate dynamic load transfer to front axle during braking.
During braking, load shifts from the rear axle to the front axle. Given mass, deceleration, center of gravity height, and wheelb...

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Estimate brake line pressure required for a given force.
Hydraulic braking systems amplify pedal input to generate braking force. Given braking force and piston area, compute the hydrau...

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Compute the required brake torque at wheel to stop the car
Brake torque defines how effectively braking force translates into wheel deceleration. Given braking force and wheel radius, det...

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Compute braking force using vehicle mass and acceleration.
Compute braking force required to stop a vehicle of mass 'm' and with acceleration 'a' Remember: F = m × a.

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Compute vehicle stopping distance using initial speed and constant deceleration.
Given vehicle speed v (m/s) and constant deceleration a (m/s²), compute stopping distance Remember: d = v² / (2a)

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Compute the largest number with a given integer complexity
Cody Problems 42831 and 42834 ask us to compute integer complexity, the smallest number of 1s needed to construct a number with ...

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Compute the Lagarias Riemann Hypothesis sequence
Write a function that takes an input number and produces a sequence (i.e., all values up to and including the th value) compute...

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Compute the unitary totient of a number
The totient function , the subject of Cody Problems 656 and 50182, gives the number of integers smaller than that are relativel...

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Sum the unitary divisors of a number
Cody Problems 1933 and 46898 deal with , the sum of divisors function. This problem deals with , the sum of unitary divisors fun...

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Count the unitary divisors of a number
Cody Problem 56738 asks for a list of the unitary divisors of a number. For this problem, write a function to count the unitary ...

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Count estrangements
Recently I made a puzzle for my wife that included a cryptogram, which involves an arrangement of the letters A through Z. I use...

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Trap a knight
Consider a knight on an infinite chessboard labeled with numbers spiraling outward. A knight starting on the square labeled 1 ca...

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Flip the parity of digits in a decimal expansion
The number 349 has the decimal expansion . If we change the even digits from positive to negative, then the number becomes 269 (...

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Determine whether a number is practical
A number is practical if all smaller numbers can be written as a sum of the proper divisors of . The number 24 is practical bec...

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Generate the Figure-Figure sequence
After discussing Scott Kim’s FIGURE-FIGURE Figure (below) in Gödel, Escher, Bach, Douglas Hofstadter introduced an integer seque...

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Determine whether the input is an anagram number
In Cody Problem 44293, Mehmet OZC asks us to spell numbers as words. For example, 67 would be “sixty-seven” and 76 would be “sev...

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Compute a determinant
Write a function to compute the determinant of an x matrix with diagonal entries equal to an integer and other entries equal ...

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