Number Series Puzzles
A row of numbers, one rule running underneath, and a gap at the end. Work out what turns each term into the next, then choose the number that continues it — and see the rule named, with a reason for every wrong option.
Also known as number sequences, find the next number and series completion.
Find The Rule Running Through The Numbers
A number series shows a run of numbers that follow a hidden rule and asks what comes next. The rule can be arithmetic — a constant difference — or multiplicative, alternating, based on squares, primes, or a combination. The differences between terms are the first place to look.
How To Solve Number Series Puzzles
- Write the differences between neighbouring terms.
- If the differences are constant, the rule is arithmetic.
- If not, difference them again — second differences reveal quadratic rules.
- Check ratios when differences grow fast.
- Test your rule on every term before answering.
Differences first, always. One subtraction pass turns most series from mystery to arithmetic, and the wrong options are built to punish skipping it.
| Family | What it covers |
|---|---|
| Steady gaps | undefined |
| Growing gaps | undefined |
| Multiplying | undefined |
| Two-step rules | undefined |
| Square numbers | undefined |
| Cube numbers | undefined |
| Looking back two | undefined |
| Two series woven | undefined |
| Prime numbers | undefined |
| Alternating operations | undefined |
Ten Rule Families
Every series here comes from a named rule family — the same families, narrated in the explanation. Once you can name a family from its differences, you can read any series the generator produces.
Number Series Puzzles Frequently Asked Questions
How do you find the rule in a number series?
Work through a fixed order rather than staring at it. Write the differences between consecutive terms underneath; if they are equal, the rule is a constant addition. If not, take differences again — a constant second difference means the gap grows steadily. If the series grows faster than that, divide instead of subtracting to test for a ratio. Only then check squares, cubes and primes, and last of all try reading alternate terms as two woven series.
What are the most common number series patterns?
Six cover most of what you will meet: a constant difference, a difference that grows by a fixed amount, a constant ratio, a two-step rule such as multiply then add, the well-known families of squares and cubes, and each term being the sum of the two before it. Two more turn up often enough to be worth knowing: prime numbers, and two separate series interleaved.
Why does my answer fit but still get marked wrong?
Usually because the rule was tested on too few terms. Almost any two terms can be joined by several rules, and three by more than one, so a rule that fits the start and fails later is not the rule. The other common cause is finding a rule that works but is not the simplest one available — series are built on the simplest consistent rule, and that is the convention every setter follows.
Are the puzzles here the same every time?
No. Each of the 60 patterns names a rule family, and the numbers are generated fresh from the seed, so the same pattern gives you a different series every visit. The one you played keeps a permanent link if you want to send it to someone or come back to it.
What is the difference between a number series and a wrong number puzzle?
A number series shows a run that obeys its rule all the way through and asks you to continue it. A wrong number puzzle shows a run in which exactly one term has been broken and asks you to find it. The skill is the same — identify the rule — but the second is harder, because you cannot trust any single term until you have tested it.
How can I get faster at number series?
Work through the same checks in the same order every time rather than hunting for inspiration. Look at the gaps between terms first; if the gaps are not constant, look at the gaps between the gaps; then try ratios; then check whether each term is built from the two before it. Most series fall to one of those four.
What is a number series?
A row of numbers built by a rule, with one of them missing — usually the next one. The rule might add a fixed amount, multiply, square, alternate between two operations, or weave two separate sequences together. You are not asked to recognise the numbers, only to work out what turns each one into the next.