What is inductive reasoning?

Inductive reasoning is the ability to infer a general rule from specific examples and use it to predict what comes next.

Tests measure it with number series, letter series, figure sequences and "which belongs to the group" items. It is a core part of fluid intelligence, and unlike deduction its conclusions are only ever probable: a new example could always break the rule.

By What's Your IQ · Published 3 Oct 2026 · Updated 3 Oct 2026

Format: Series or sets with a hidden rule and 4–5 options
Question types: Number series, letter series, find the rule, figure series
Typical employer test: 20–30 items in 20–30 minutes
Measures: Pattern detection, hypothesis testing, fluid reasoning
This test: 12 puzzles, 12 minutes, free, explained answers

INDUCTION · THIS TEST

Examples → rule

3, 6, 9, 12 … so: +3 each timeThe conclusion is the best explanation of what you've seen. It's probable, not guaranteed: the next term could be 16 if the real rule were something stranger.

DEDUCTION · THE OPPOSITE DIRECTION

Rule → example

"Add 3 each time", start at 3 … so: 15 is fifthGiven the rule, the answer is certain. That's what logical and syllogism tests measure.

The difference table

The fastest general method for number series. Subtract neighbours until a row stops changing, then build back up.

SERIES

2510172637

Δ1

357911

Δ2

2222

Next: 37.The second differences are constant (2). Extend that row, add it to the last first difference (9 + 2 = 11), then add that to the last term.

Six patterns to check first

Simon and Kotovsky (1963) showed most series are built from a few repeating operations. Try them in this order.

1Constant step4, 9, 14, 19Add or subtract the same amount. First differences are equal.

2Growing step2, 3, 5, 8, 12The step itself changes by a fixed amount. Second differences are equal.

3Multiply3, 6, 12, 24Each term is a fixed multiple of the last. Ratios are equal.

4Squares & cubes1, 4, 9, 16 · 1, 8, 27Look for n² or n³, sometimes plus or minus a constant.

5Alternating5, 10, 8, 16, 14Two rules take turns, or two series are interleaved. Split odd and even positions.

6Add the previous two1, 1, 2, 3, 5, 8Each term depends on the two before it (Fibonacci-style).

Take the test

12 puzzles · 12 minutes · scratch paper allowed

Number series6 puzzlesLetter series3 puzzlesFind the rule3 puzzles: which one belongs?

Puzzle 1 of 12Number series

00:00

What comes next?

371115?

0/12Work through the six patterns, then go again.Weakest: number series (0/6) · 29854925:31

Number series0/6Letter series0/3Find the rule0/3

3, 7, 11, 15, ?Answer 19 · you chose nothingAdd 4 each time: 15 + 4 = 19.

2, 6, 18, 54, ?Answer 162 · you chose nothingMultiply by 3 each time: 54 × 3 = 162.

1, 4, 9, 16, 25, ?Answer 36 · you chose nothingSquare numbers: 1², 2², 3², 4², 5², so 6² = 36.

2, 3, 5, 8, 12, 17, ?Answer 23 · you chose nothingThe gaps grow by one: +1, +2, +3, +4, +5, then +6 gives 23.

5, 10, 8, 16, 14, ?Answer 28 · you chose nothingTwo steps alternate: ×2, then −2. Next is 14 × 2 = 28.

1, 1, 2, 3, 5, 8, 13, ?Answer 21 · you chose nothingEach term is the sum of the two before (Fibonacci): 8 + 13 = 21.

A, C, E, G, ?Answer I · you chose nothingSkip one letter each time: A, (B), C, (D), E … G, (H), I.

Z, X, U, Q, ?Answer L · you chose nothingGoing backwards by 2, 3, 4, then 5: Q (17) − 5 = 12, which is L.

B, D, G, K, ?Answer P · you chose nothingForwards by 2, 3, 4, then 5: K (11) + 5 = 16, which is P.

12, 18, 30, 42 · ?Answer 48 · you chose nothingEvery number is a multiple of 6. Only 48 is.

7, 13, 19, 31 · ?Answer 23 · you chose nothingEvery number is prime. 21, 27 and 33 all divide by 3; 23 is prime.

121, 4334, 707, 58985 · ?Answer 6116 · you chose nothingEvery number reads the same backwards (a palindrome). Only 6116 does.

WASON, 1960

Test the cases that could prove you wrong.

In the original 2-4-6 study, most people announced a wrong rule at least once, usually something like "even numbers rising by two". They kept testing triples that fitted their guess and never one that didn't.

6 / 29found the rule without a wrong guessWason (1960) [1]

On a test, this means:Once a rule fits, check it against the last term and every option. If two options fit, your rule is too loose.

How to solve a number series with a difference table

1Write the differences between each pair of neighbouring numbers.
2If those differences aren't constant, take the differences of the differences.
3When a row becomes constant, extend it by one and add back up to get the next term. If no row settles, try ratios instead.

Keep going

Abstract reasoningInductive rules in shapes instead of numbers.Open

Numerical reasoningApply number skills to tables and charts.Open

Logical reasoningThe deductive counterpart: rules to certain answers.Open

References

Wason, P. C. (1960). On the failure to eliminate hypotheses in a conceptual task. Quarterly Journal of Experimental Psychology, 12(3), 129–140.
Klauer, K. J., & Phye, G. D. (2008). Inductive reasoning: A training approach. Review of Educational Research, 78(1), 85–123.
Heit, E. (2000). Properties of inductive reasoning. Psychonomic Bulletin & Review, 7(4), 569–592.
Simon, H. A., & Kotovsky, K. (1963). Human acquisition of concepts for sequential patterns. Psychological Review, 70(6), 534–546.

From a few examples to the rule.