Feynman School

Showcase

Real quests, built from real questions.

Each of these started as one question. Here is the route our engine planned and one of its live labs, with the situation it’s set in. Sign in to take the whole quest.

Circuits · 5 steps · 41 min

Why Removing a Resistor Raises Resistance

Predict and calculate how series and branching paths change a meter’s resistance reading.

  1. 1Remove a branch, raise the reading?Predict and observe that disconnecting the 330 Ω branch raises the whole-network reading from 232 Ω to 320 Ω.
  2. 2Find the branch pair firstCalculate the resistance of the two branches together, then add the resistor that every path crosses.
  3. 3Catch the wrong meter predictionUse path tracing and a calculation to check a changed network before trusting a bench reading.
  4. 4Which pair can you replace first?Reduce two unbranched branches before combining them, then add the resistor outside the split to obtain 250 Ω.
  5. 5Reduce a split inside a branchIndependently reduce an inner parallel pair, its branch's series resistor, and the outer parallel pair to obtain 100 Ω.
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The situation

The bench network reads 232 Ω with both branches connected. You can disconnect just the 330 Ω branch.

Physics · ~3 min · live model
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Coupled Oscillations · 4 steps · 27 min

Two Carts, One Spring That Sleeps

Predict which shared motion leaves the joining spring idle and which makes the carts oscillate faster.

  1. 1Make the Middle Spring SleepPredict and observe that moving both carts 2 cm right leaves the joining spring unstretched throughout the motion.
  2. 2Pull Apart, Change the RhythmExplain why equal-and-opposite motion engages the joining spring and produces a faster oscillation.
  3. 3Find the Two Shared RhythmsUse the forces in each motion to find its angular frequency and identify both normal modes.
  4. 4Release Just One CartSplit a one-cart release into two patterns and predict that the carts will not continue moving together or exactly oppositely.
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The situation

The same carts now start 2 cm away from equilibrium in opposite directions and are released from rest; first inspect stretch, then the resulting spring forces.

Physics · ~3 min · live model
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Fluid dynamics and projectile motion · 4 steps · 27 min

Why a Spinning Baseball Breaks

Predict a pitch’s spin-related break and distinguish it from ordinary gravitational drop.

  1. 1Flip the Spin, Keep the ThrowNotice that reversing spin changes the ball’s path even though its release and gravity are unchanged.
  2. 2Name the Extra PushExplain the path difference using an aerodynamic force associated with spin, without changing gravity.
  3. 3Break Is Not Total DropUse a no-spin comparison to identify spin-related break rather than mistaking all downward motion for a Magnus effect.
  4. 4Turn the Spin AxisApply the same force reasoning when the spin-related deflection is sideways rather than vertical.
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The situation

The same pitch comparison now shows force arrows. The Magnus force—the sideways or vertical aerodynamic push associated with a spinning ball moving through air—points upward for backspin and downward for topspin in this side-view model.

Physics · ~3 min · live model
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Noether’s theorem and orbital mechanics · 4 steps · 27 min

Why Earth Speeds Up Near the Sun

Predict Earth’s orbital speed, identify what stays constant, and explain why.

  1. 1The Faster Part of Earth’s OrbitNotice that Earth moves faster when it is closer to the Sun, while distance multiplied by speed is nearly unchanged at the two turning points.
  2. 2Rotate the Orbit, Keep the RuleConnect the nearly constant product to angular momentum and to the fact that the Sun’s gravity has no preferred direction around it.
  3. 3Two Symmetries, Two Conserved QuantitiesDistinguish rotational symmetry’s angular momentum from time-translation symmetry’s energy, then state the assumptions Noether’s theorem needs.
  4. 4A New System, A New Conservation TestApply Noether’s theorem to an isolated interaction and distinguish linear momentum from orbital angular momentum.
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The situation

Earth is 152.1 million km from the Sun and moving at 29.29 km/s at aphelion. At perihelion it is 147.1 million km away.

Physics · ~3 min · live model
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Monty Hall problem · 3 steps · 16 min

The Door the Host Cannot Open

See why switching wins more often, without needing probability formulas.

  1. 1Two unopened doors, unequal chances.Predict whether the host's reveal makes staying and switching equally good.
  2. 2Move the prize, not your pick.Check the stay and switch result for each possible prize location.
  3. 3When does switching really win?Explain why switching wins in two of the three placements and identify the host rule it needs.
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The situation

You pick Door 1; the host reveals a goat behind another door, leaving two doors closed.

Maths · ~3 min · live model
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Language model text generation. · 4 steps · 26 min

Why ChatGPT Changes Its Next Word

See how ChatGPT chooses its next piece of text and predict what temperature changes.

  1. 1Two endings, one prompt.Explain why learned language patterns make some endings more familiar without making any ending certain.
  2. 2Pick a piece, then predict again.Trace how a scored text piece is selected and creates a new prediction point.
  3. 3Turn the temperature dial.Predict how temperature changes selection when the prompt and candidate scores stay fixed.
  4. 4Explain the surprising reply.Explain why a fluent continuation may vary without assuming the model verified it.
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The situation

Show “The cat sat on the,” ask the learner to choose “mat” or “sofa,” then connect both familiar continuations to patterns learned during training before mentioning scores.

AI · ~3 min · live model
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Visual Linear Algebra · 4 steps · 26 min

Move Two Arrows, Move the Grid

Predict how a matrix moves an entire image grid by following two arrows.

  1. 1Why Did Every Square Move?Notice that dragging one arrow reshapes the whole grid while its center stays fixed.
  2. 2Make the Grid Tall, Then Turn ItConnect arrow lengths and directions to visible stretches and turns.
  3. 3A Turn or a Mirror?Use the arrows’ order around the center to tell a flip from a turn.
  4. 4Find the Point the Arrows Never TouchedSee the moved arrows as matrix columns and combine them to locate an unmarked point.
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The situation

On the same grid, predict the effect of lengthening the up arrow, drag it, then turn both arrows a quarter-turn and inspect where a marked square lands.

Maths · ~3 min · live model
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