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William


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Semi-retired physicist with interests in numerical modeling and mathematics.

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Solved


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

6 hours ago

Solved


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

8 hours ago

Solved


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; ...

8 hours ago

Solved


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

9 hours ago

Solved


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...

9 hours ago

Solved


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...

3 days ago

Solved


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...

3 days ago

Solved


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...

3 days ago

Solved


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 ...

3 days ago

Solved


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

3 days ago

Solved


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...

3 days ago

Solved


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

3 days ago

Solved


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;...

3 days ago

Solved


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...

3 days ago

Solved


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...

3 days ago

Solved


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...

3 days ago

Solved


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.

3 days ago

Solved


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)

3 days ago

Solved


Gather primes
A book titled Gather that I regularly see inspired this game: make as many words as possible from the letters in the word GATHER...

10 days ago

Solved


Leo Bậc Thang
Bạn đang leo cầu thang. Cần n bước để lên đến đỉnh. Mỗi lần bạn có thể leo 1 hoặc 2 bước. Hỏi có bao nhiêu cách khác nhau để le...

12 days ago

Solved


Find nth triangular number.
Calculate the triangular number of given integer n.

13 days ago

Solved


Find record values in a sequence
Write a function to find the record values in a sequence—that is, the largest values seen since the start. For example, if the s...

16 days ago

Solved


[Mảng 1 Chiều Cơ Bản]. Bài 5. In phần tử
Cho mảng số nguyên A[] gồm N phần tử, nhiệm vụ của bạn là in ra các phần tử là số chẵn ở chỉ số chẵn, nếu mảng không tồn tại phầ...

20 days ago

Solved


Scaling vertically parabola by evaluating its area over an interval
Let p be a quadratic polynomial, with its axis of symmetry being the y-axis. Considering the vertical shift of its vertex to the...

20 days ago

Solved


[Mảng 1 Chiều Cơ Bản]. Bài 4. Lớn hơn, nhỏ hơn
Cho mảng số nguyên A[] gồm N phần tử và số nguyên X , hãy đếm xem trong mảng có bao nhiêu số lớn hơn X và bao nhiêu số nhỏ hơn X...

21 days ago

Solved


[Mảng 1 Chiều Cơ Bản]. Bài 2. Trung bình cộng nguyên tố
Cho mảng số nguyên A[] gồm N phần tử, nhiệm vụ của bạn là tính trung bình cộng của các số là số nguyên tố trong dãy. Dữ liệu đảm...

21 days ago

Solved


[Mảng 1 Chiều Cơ Bản]. Bài 1. Chẵn lẻ
Cho mảng số nguyên A[] gồm N phần tử, nhiệm vụ của bạn là đếm xem trong mảng có bao nhiêu số chẵn, bao nhiêu số lẻ, tổng các phầ...

21 days ago

Solved


[Mảng 1 Chiều Cơ Bản]. Bài 3. Số nhỏ nhất
Cho mảng số nguyên A[] gồm N phần tử, hãy đếm xem trong mảng của bạn có bao nhiêu số có cùng giá trị nhỏ nhất. Ví dụ mảng A = {1...

21 days ago

Solved


Extract numbers using a decaying sieve
The Sieve of Eratosthenes is one method of determining primes. Starting with 2, one keeps 2 and removes 2x2, 3x2, 4x2, etc. Then...

25 days ago

Solved


Scaling vertically functions
Given a real function by the 1×n array, x, of inputs and the 1×n array, y, of outputs, consider shifting vertically its graph by...

25 days ago

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