Lesson 3 of 7
Thinking takes tokens
10 min read
Ask a model a tricky arithmetic question and demand just the answer — no working — and it often flubs it. Let it write out its steps first and it sails through. Same model, same question. Why does showing its work make it smarter?
One token, one slice of thinking
Here's a fact about how these models run: each token the model writes gets the same fixed amount of computing — one quick pass through the network. There's no pause button and no hidden scratchpad off to the side. A hard problem that needs several steps of reasoning can't be crammed into that single pass. Forced to blurt the answer in one token, the model has one slice of thinking to do all the work — and for a multi-step problem, that isn't enough.
A model does a fixed amount of computing per token. A one-token answer gets exactly one slice of thinking — no matter how hard the question is.
Give it room to work
So the fix is almost silly: let it write more. When the model reasons out loud — “3 rows of 8 is 24; take away 5; that leaves 19” — each of those tokens is another slice of computing, and the earlier steps become notes it can read back. The written words are the scratchpad. Try both below: force an instant answer, then let it think first, on the same question.
Letting a model think in writing isn't just for show — the extra tokens are extra computing. More room to work, spread over more tokens, is literally more thinking applied to the problem.
Turn the thinking room up and down
The fix comes with a dial. Below you control two things at once: how hard the problem is, and how much room to think you allow — how many steps of working the model may write before it answers. Give a hard problem too little room and it has to blurt a rushed guess; give it enough and the working reaches the answer. And notice: room left over past what the problem needs just sits there, unused.
How much room a problem needs isn't fixed — it grows with the problem. An easy one finishes in a single step; a hard one only comes out right once you give it enough steps to get there.
Why harder problems need more room
So a model's “thinking” isn't a mood you can coax out of it — it's room, counted in written steps, each step a fixed slice of computing. A harder problem simply needs more of those steps, and if it isn't allowed to write them, it can't get there; no amount of confidence fills the gap. That's the real reason demanding a snappy one-line answer to a genuinely hard question so often buys you a wrong one.
This is the whole idea behind reasoning models: they're trained to produce a long private stretch of working before the final answer, spending as many tokens “thinking” as a hard problem needs. The rest of this course is about how a model learns to use that room well.
Recap
- —A model spends a fixed amount of computing on each token — one pass, no hidden scratchpad
- —Forced to answer in a single token, it can't do multi-step problems — there's no room for the steps
- —Letting it write its reasoning out gives it more tokens, and each token is more computing — showing its work is thinking
- —How much room a problem needs scales with its difficulty — hard problems only come out right with enough steps
A model keeps getting a multi-step word problem wrong when you ask for just the final number. What's the single most reliable fix?
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