Free games › Sequence › How a solver cracks it
How a solver cracks number sequences
A sequence solver does not recognise a pattern the way a person feels it. It tests a short list of rule families in a fixed order and takes the first one that fits every term it can see.
The method
- Take the gaps. If every gap between neighbours is the same, the rule is a constant step.
- Check for a constant multiplier. If each term is the previous one times the same number, it is a ratio.
- Take the gaps of the gaps. If those are constant, the gaps themselves grow steadily.
- Test the sum of the two before. Each term equal to the previous two added together.
- Split into two streams. Odd-numbered and even-numbered terms may each follow their own steady step.
- Test an alternating operation. For example times 2, then minus 3, repeating.
A rule only counts if it reproduces every visible term, and then it predicts the next one. That is the part to copy: commit to a rule, then check it against terms you did not use to form it.
Worked examples
- 8, 10, 12, 14, 16, 18, ? The solver answers 20. Each term is the one before it plus 2.
- 1, 2, 4, 8, 16, 32, ? The solver answers 64. Each term is the one before it times 2.
- 4, 8, 15, 25, 38, 54, ? The solver answers 73. The gaps grow by 3 each time.
- 5, 6, 11, 17, 28, 45, ? The solver answers 73. Each term is the sum of the two before it.
- 4, 71, 7, 68, 10, 65, ? The solver answers 13. Two interleaved sequences, each stepping by a fixed amount.
- 2, 4, 3, 6, 5, 10, ? The solver answers 9. The operation alternates: times 2, then minus 1.
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