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Rule induction

Pattern-Sequence Induction

A sequence of colored shapes follows a hidden rule (e.g., "alternate red/blue, every third is green"). You see some of the sequence. Predict the next item. We start with simple rules and increase complexity until you miss.

What makes this one different

We fit a personal rule-difficulty curve — your accuracy vs. rule complexity. That curve is more informative than a single "max level reached" number.

Level 1
Score 0
Sequence so far:
What comes next?
Ad slot.

Accuracy across complexity

History

No sessions yet.

What problem does it solve?

Rule induction — figuring out the hidden rule that generates a sequence — is one of the core components of fluid intelligence. The classic "find the next number" puzzles tap into it. We provide a parameterized version where rule complexity grows in a controlled way.

Who is this for

How to interpret your results

Accuracy curve: where does it drop? That's your rule-complexity ceiling. Most adults plateau around complexity 5–6.

Limitations

  • The visual symbols (color/shape) are arbitrary. If you learn one rule type really well, you'll spot similar patterns faster.
  • Some users may brute-force guess rather than truly reason. The complexity curve still captures real performance.

FAQ

Can I get feedback on what the rule was?

Yes — after each trial, if you miss, we reveal the rule. That's the best way to learn pattern recognition.

Does speed matter?

Not directly. We don't time trials. If you need time to think, take it — the score reflects accuracy, not speed.

How do I use Pattern-Sequence Induction step by step without mistakes?Follow the order given in the usage section: Watch colored shapes follow hidden rules. Predict the next. Rule complexity grows — and we plot the difficulty curve. The step-by-step part matters less than the unit check that sits inside it. Confirm every unit matches the thing you are actually trying to measure before you press calculate - that single check catches more wrong answers than any other habit, and it costs about ten seconds.
What are the common mistakes when using Pattern-Sequence Induction?Most common mistakes come down to four habits: entering 20 when the field expects 0.2 because the field is a percentage; leaving a field blank and accepting the default without checking what it stands for; changing one input and reading a result that was calculated before the change; and quoting the output as an exact figure when the page describes it as a reference estimate. Press calculate again after any edit, and treat the number as a reference point rather than a final answer.
How do I read the result from Pattern-Sequence Induction?Read the final figure first, then come back to this section for the conditions behind it: Accuracy curve : where does it drop? That's your rule-complexity ceiling. Most adults plateau around complexity 5–6. Keep two things apart: the number itself, which comes from the values you typed, and the assumptions it depends on, which decide whether that number is meaningful. The page sets out what a higher or lower result means for your case, so check that direction as well as the magnitude.
Can I act on the Pattern-Sequence Induction result directly?Treat it as one reference sheet before you decide, rather than as the answer itself: The visual symbols (color/shape) are arbitrary. If you learn one rule type really well, you'll spot similar patterns faster. Some users may brute-force guess rather than truly reason. The complexity curve still captures real performance. The output describes a magnitude under the conditions you entered. It does not include what it actually costs to act, what might change while you act, or how the other side behaves. Before you commit, compare the result against reality and note which assumptions do not hold where you are.
What inputs does Pattern-Sequence Induction need?The inputs for this tool sit in the form area of the page - fill them in one at a time as prompted. Before you start, check that each one uses the unit you actually measured: mismatched units are the most common source of a wrong answer here.
What should I check before I run Pattern-Sequence Induction?Three checks pay for themselves. First, confirm the question you need answered is really inside the scope of this tool rather than a neighbouring one. Second, confirm that the figures you have are drawn from the same source and the same period - mixing monthly and annual numbers, or two different definitions of the same quantity, quietly distorts the result. Third, keep the key inputs written down, so that later you can tell which set of numbers produced a figure you are about to quote.