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Easy Sequences 39: Perfect Squares in Pascal's Triangle
Consider the 2nd, 3rd and 4th diagonals of the Pascal's Triangle, shown highlighted below: ...
alrededor de 11 horas hace
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Number of paths on a 3d grid
This problem is inspired by <https://www.mathworks.com/matlabcentral/cody/problems/1483-number-of-paths-on-a-grid>, which you mi...
alrededor de 12 horas hace
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Number of paths on a grid
Consider a grid formed by n vertices vertically down, and m vertices horizontally right. Your starting point is at the top lef...
alrededor de 12 horas hace
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Newton’s First Law – Net Force in Equilibrium
At a manufacturing plant operated by Reliance Industries in Jamnagar, a heavy equipment box rests on the factory floor. Even th...
1 día hace
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Newton’s Second Law – Gravitational Force on a Falling Object
During a relief mission organized by the Indian Air Force, supply packages are dropped from aircraft to remote flood-affected ar...
1 día hace
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Newton’s Second Law – Acceleration of Connected Objects
Engineers at Boston Dynamics are testing two robots connected by a rope on a frictionless surface. Robot A pulls Robot B using ...
1 día hace
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Newton’s Second Law – Force Produced by a Car Engine
Automotive engineers at Tata Motors are testing a new electric car prototype on a straight test track in Pune. The engineers wa...
1 día hace
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Newton’s Third Law – Action and Reaction in Rocket Launch
Scientists at SpaceX are testing a rocket engine before launch from their facility. When the rocket pushes exhaust gases downwa...
1 día hace
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Newton’s Second Law – Normal Force in an Accelerating Elevator
Engineers at Otis Elevator Company are testing a new high-speed elevator installed in the Burj Khalifa. When the elevator accel...
1 día hace
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Newton’s Second Law – Motion on an Inclined Plane
In the mountainous region near Manali, a rescue team is testing a motorized emergency vehicle designed to climb steep slopes. E...
1 día hace
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Newton’s First Law – Force Needed to Start Motion
At Indira Gandhi International Airport, a heavy suitcase is sitting on a stationary conveyor belt. The belt is initially at rest...
1 día hace
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Newton’s Second Law – Acceleration of a Mars Rover
At NASA's robotics laboratory, engineers are preparing a prototype rover for a future mission to Mars. Before sending the rover...
1 día hace
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Newton’s Second Law – Force Required to Accelerate a Rocket Cart
At ISRO's training center, engineering students are testing a small rocket-powered cart on a straight frictionless track. The ca...
1 día hace
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Given a Polyshape_01 (ps) Return its Perimeter, Area, and Centroid.
Return the perimeter (P) of a polyshape object, which is the sum of the lengths of its boundaries. Return the total area (A) of...
1 día hace
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5-year Annedversaries
This is the Bonus Round problem for the 2025 Cody Contest. Attend the watch party on Friday, March 27 to see how 6 champions fro...
3 días hace
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Angular Velocity of a Falling Rod Pivoted at One End (Energy + Rotation)
Engineers at Indian Institute of Technology Bombay are designing a rotating docking arm for a future space station. The arm is m...
10 días hace
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Angular Velocity Required to Create Artificial Gravity
Scientists at NASA and Indian Space Research Organisation are designing a rotating space station ring to simulate Earth-like gra...
10 días hace
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Moment of Inertia Using Parallel Axis Theorem
Engineers at Indian Space Research Organisation are designing a satellite with extendable robotic arms. When the arms extend out...
10 días hace
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Acceleration in a Symmetric Double-Pulley Constraint System
Engineers at Indian Institute of Technology Kanpur are designing a precision counterweight system for high-speed elevators. The ...
10 días hace
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Tension in String for Circular Motion (Advanced Rotational Dynamics)
At the astronaut training facility of Indian Space Research Organisation, astronauts are trained using a rotating centrifuge. Th...
10 días hace
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Angular Velocity of a Falling Rod Pivoted at One End (Energy + Rotation)
Engineers at Indian Institute of Technology Bombay are designing a rotating docking arm for a future space station. The arm is m...
10 días hace
Resuelto
Motion of a Bead Sliding on a Rotating Rod (Non-Inertial Frame Dynamics)
Scientists at Indian Space Research Organisation are testing artificial gravity inside a rotating space station module. Inside ...
10 días hace
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Acceleration of Block Relative to Ground
Researchers at Indian Space Research Organisation test cargo motion inside accelerating spacecraft ramps. Find acceleration.
10 días hace
Resuelto
Acceleration in an Atwood Machine with Massive Pulley
Engineers at Indian Institute of Technology Delhi are designing a precision elevator calibration system using two masses connect...
10 días hace
Resuelto
Velocity of a Particle Under Constant Acceleration Using Energy Methods
Scientists at CERN are testing a linear accelerator that uses electromagnetic force to accelerate charged particles along a stra...
10 días hace
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Euler primes
Historical context The great swiss mathematician Leonhard Euler found the formula to give some prime numbers. Problem...
15 días hace
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Rotating 2d curve around a vertical axis
Let p be an even-degree polynomial such that has a unique vertex (single global extremum). Consider the counterclockwise rotatio...
16 días hace
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Rotating the plane region bounded by two polynomials
Let p and q be n-degree and m-degree polynomials with n >= m >= 1. Consider clockwise rotate the plane region bounded by these t...
16 días hace
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Odd Run Sums
Given a row vector x of integers, find every maximal run of consecutive odd numbers and return a row vector containing the sum o...
20 días hace
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Comparing to scale all terms versus one term of even-degree polynomial by the same scale factor
Let p be an even-degree polynomial with positive leading coefficient. Consider the scale factor, k, that vertically transforms ...
20 días hace
