Number Sequence

💡 Number Sequence Strategy

• Write the gaps first. Subtract each number from the one after it. If those differences are constant you have an arithmetic run, and you are done in one step.
• If the gaps vary, take the gaps of the gaps. A constant second difference means the sequence is squared-based — 1, 4, 9, 16 and its cousins hide here.
• Try dividing when numbers grow fast. Anything doubling, tripling, or growing steeply is usually multiplicative rather than additive.
• Watch for two interleaved runs. Sequences like 2, 10, 4, 20, 6 are two simple patterns zipped together; read every other term.
• Check the primes and the Fibonacci run. When nothing else fits, 2·3·5·7·11 or 1·1·2·3·5·8 often does.

🧠 What Number Sequence Builds

Finding the rule behind a run of numbers is inductive reasoning — going from examples to the law that produced them — and it is a different muscle from calculating. The arithmetic involved stays deliberately light so that the challenge lives in the noticing, not in the sums. It is a strong daily exercise precisely because each puzzle takes under a minute once the rule clicks.