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Open Model Lab
ChallengesSolved 0 of 172 challenges

Pick a bounded task, then open the exact concept bench that can solve it.

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Start with Short-period matchBrowse starter paths
Best first challengeTo tryCore

Short-period match

Starting from Calm start, make the oscillator complete a shorter cycle without turning it into a wider swing. Keep the displacement graph open so the timing change stays visible.

Simple Harmonic Motion

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Starter challenge paths

Open these only when you want the next few challenge moves narrowed into one authored path.

Starter track0/10 solved

Motion and Circular Motion

Start with vector components, move into projectile paths, and then use circular motion to understand how velocity can keep changing direction.

Short-period force band is the next best challenge from Uniform Circular Motion.

Starter track0/15 solved

Rotational Mechanics

Start with torque as the turning effect of force, use centre of mass and support region for static balance, then carry the same rotational language into moment of inertia, rolling motion, and angular momentum.

Zero turn at the handle is the next best challenge from Torque.

Starter track0/12 solved

Gravity and Orbits

Start with one source mass creating a field and potential well, then use that same gravity model to explain circular speed, orbital periods, and the escape threshold.

Keep the heavier source circular is the next best challenge from Circular Orbits and Orbital Speed.

Show 16 more starter paths
Starter track0/6 solved

Oscillations and Energy

Build from one clean oscillator to energy exchange and then to driven resonance, so the same system grows without changing its core ideas.

Starter track0/10 solved

Fluid and Pressure

Start with pressure in a resting fluid, then carry that same branch through continuity, Bernoulli, buoyancy, and drag-limited motion.

Starter track0/19 solved

Waves

Use oscillation as the entry point, lock down wave speed and wavelength, carry that into longitudinal sound and pitch-versus-loudness cues, add beats as the nearby-frequency superposition bridge, then move into Doppler shifts, interference, standing-wave patterns, and open-vs-closed air-column resonance without losing the live connection between motion and graph.

Starter track0/8 solved

Thermodynamics and Kinetic Theory

Start with temperature-versus-internal-energy bookkeeping, reuse that particle story for gas pressure, then follow energy transfer into heating curves and phase-change shelves.

Starter track0/7 solved

Electricity

Start with source charges and voltage, then carry that same circuit story into current, power, branch behavior, and equivalent resistance.

Starter track0/6 solved

Magnetism

Start with current-made magnetic fields, turn changing flux into induced emf with Faraday and Lenz, and then reuse that same field direction story to explain magnetic force on charges and currents.

Starter track0/11 solved

Sound and Acoustics

Stay on the sound branch long enough that longitudinal motion, pitch-versus-loudness cues, beats, Doppler shifts, and open-vs-closed air-column resonance feel like one acoustics path instead of isolated pages.

Starter track0/10 solved

Wave Optics

Follow the bounded wave-optics branch from polarization into diffraction, double-slit interference, color-dependent refraction, and imaging limits so the newer optics pages read like one compact path instead of isolated stops.

Starter track0/10 solved

Modern Physics

Follow the bounded modern-physics branch from threshold emission into line spectra, matter waves, the Bohr hydrogen model, and half-life so the new concept set reads like one path instead of five isolated pages.

Starter track0/6 solved

Functions and Change

Keep the first math path compact: read parent-curve moves first, then rational asymptotes and domain breaks, then exponential growth and decay, local slope, visible limit behavior, and finally accumulation so change stays graph-first all the way through.

Starter track0/6 solved

Complex and Parametric Motion

Start with complex numbers as points on one plane, turn that plane into unit-circle and polar-coordinate geometry, deepen that same bench into trig identities and inverse-angle reasoning, then carry the coordinate language into motion traced from x(t) and y(t).

Starter track0/4 solved

Vectors and Motion Bridge

Start with vectors as geometric objects on a 2D plane, then carry the same component language into the existing motion-facing vectors bench.

Starter track0/4 solved

Rates and Equilibrium

Start with successful collisions setting reaction rate, then reuse the same chemistry language inside a reversible system that re-balances after a disturbance.

Starter track0/3 solved

Stoichiometry and Yield

Start with one visible reaction recipe, use the lower batch cap to identify the limiting reagent, and then compare actual output with the same theoretical marker.

Starter track0/6 solved

Solutions and pH

Start with concentration in one beaker, add solubility limits and saturation, then reuse that same solution language to read pH, buffers, and neutralization.

Starter track0/5 solved

Algorithms and Search Foundations

Start with visible list work, reuse that search language for binary search, and then carry the branch into one live graph bench for adjacency, BFS, DFS, and visited-state behavior.

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Showing 5 of 172 challenge entries. Active filters: Algorithms and Search Foundations.

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Algorithms and SearchTo tryCore

Use insertion where it pays off

Build a case where insertion sort finishes a nearly sorted list with very few writes.

Sorting and Algorithmic Trade-offs

Path: Algorithms and Search Foundations

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Algorithms and SearchTo tryCore

Find a far-right target fast

Build a large ordered list where the target sits near the far-right edge, but binary search still finds it in five checks or fewer.

Binary Search / Halving the Search Space

Path: Algorithms and Search Foundations

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Algorithms and SearchTo tryCore

Build a wider first frontier

Start from the hub-and-detours graph at C, keep the adjacency cue visible, and explain which direct neighbors make the first frontier wider than the edge start.

Graph Representation and Adjacency Intuition

Path: Algorithms and Search Foundations

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Algorithms and SearchTo tryCore

Build a wide layered frontier

Start from the hub-and-detours graph at C, keep BFS mode on, and explain why the frontier widens before the target is reached without breaking layer order.

Breadth-First Search and Layered Frontiers

Path: Algorithms and Search Foundations

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Show 1 more core challenges
Algorithms and SearchTo tryCore

Build a deep backtracking branch

Switch to the bridge-cycle DFS scene, keep DFS mode on, and explain why the current depth can rise before the search backs up instead of looping through the cycle.

Depth-First Search and Backtracking Paths

Path: Algorithms and Search Foundations

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