Brainback
product · the hint ladder

Five rungs. All the way up. None to the answer.

Each hint is prescribed — the concept, then the tool, then the setup, then the first computational step, then the second-to-last. There is no rung six.

L0L1L2L3L4the answer — locked↓ where the answer would be
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A real Brainback problem. Real hint ladder text.

Click to unlock each rung. Each one costs points. Level 6 is red-lined — try to unlock it and see what happens.

Related rates · problem set 4, Q7brain points spent · 0

A ladder 10 ft long leans against a wall. The bottom slides away from the wall at 2 ft/s. How fast is the top sliding down when the bottom is 6 ft from the wall?

  1. rung 6 · the answerunavailable
each rung takes you closer — none of them takes you there

Ask any AI assistant for a hint on a math problem and you get a random walk. Sometimes it names the concept. Sometimes it works out half the problem. Sometimes it gives you the answer wrapped in a question mark. The variance is high and the ceiling is uncontrollable.

The hint ladder replaces that variance with structure. Each rung is calibrated to name a piece of scaffolding of a specific size. You know what you’re going to get. You can decide whether it’s worth ten Brain points.


The economics

Each hint costs 10 Brain points. You start with 100, regenerate 50 a day, and cap at 200. The math works out to a reliable ten hints per day if you use them steadily, and roughly twenty available in a burst if you’ve been saving.

We do not offer unlimited hints. Unlimited hints turn hints into an answer button. The cost is what makes each hint intentional.

What each rung does

Level 1 — name the concept

The general area. “This is a related-rates problem.” “This is stoichiometry.” “This is an argument from analogy.”

Level 2 — name the tool

The specific technique. “Differentiate both sides with respect to t.” “Use the mole ratio from the balanced equation.” “Identify the disanalogy.”

Level 3 — show the setup

How to structure the work. “Label each quantity with its rate.” “Convert grams to moles first.” “List the assumed similarities before naming the disanalogy.”

Level 4 — first computational step

The first move on paper. “Substitute the known rates.” “Compute the moles of oxygen used.” “Rank the assumed similarities by strength.”

Level 5 — second-to-last step

The last scaffolded step. “You now have dV/dt in terms of dr/dt at the moment r = 5 cm.” “You now have moles of product; the last conversion is to grams.” “You now have your ranked list; the weakest similarity is the crux of the disanalogy.”


What level 6 would be

Level 6 does not exist. Level 6 would be the answer. Level 5 is the last rung. The last step, the one that actually costs you something, is always yours.

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