Number Patterns
Spot the rule behind each sequence with a free, browser-based logic game. Arithmetic, geometric, square, and Fibonacci patterns included.
Logic & PuzzlesNumber Sequences
A pattern game that rewards ruling out bad rules fast. Below: the three families of sequences and how to test each one.
Choose your difficulty
Pick a level to start playing. You can switch at any time.
How to play
Work out what comes next in the sequence, then tap the correct number.
Tip: your progress and best score are saved in this browser only.
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Logic & PuzzlesWhat you are actually practicing
A number sequence is a compression test: a rule has been used to generate the list, and your job is to recover it from a handful of terms. This game draws on three families. An arithmetic sequence adds the same step every time. A geometric sequence multiplies by the same factor. A square sequence is built from n², usually with a constant offset.
The skill being trained is not arithmetic. It is the discipline of forming a hypothesis and then checking it against every term you can see, rather than against the first two.
How the game works
You see four numbers and must produce the fifth. Four choices, a countdown, and an immediate reveal when you miss. Your score and best score are stored in this browser only.
Easy uses arithmetic sequences only. Medium mixes in geometric ones. Hard adds square patterns, so the jump between terms grows instead of staying constant — the point where most players guess instead of testing.
The three families, and how to test each
Arithmetic: subtract neighbours. 14, 20, 26, 32 gives differences of 6, 6, 6. The rule is +6, so the next term is 38. If the differences are not constant, it is not arithmetic.
Geometric: divide neighbours. 3, 6, 12, 24 gives ratios of 2, 2, 2. The rule is ×2, so the next term is 48. If the ratios are not constant, it is not geometric.
Squares: compare against n². 5, 10, 17, 26 looks irregular until you notice it is n² + 1 for n = 2, 3, 4, 5. The next term is 6² + 1 = 37. When neither differences nor ratios settle down, try subtracting the square numbers.
Strategies that actually move your score
Compute differences first, always. One subtraction row settles most arithmetic cases instantly and costs almost nothing.
Test the rule against the last term. A rule that explains 14 → 20 → 26 but predicts the wrong fourth term is not the rule. Any hypothesis must survive every term shown.
Watch for growing gaps. When the gap between terms gets wider, reach for multiplication or squares before trying ever-larger additions.
Common mistakes, and the fix for each
Mistake: trusting two terms. Almost any rule fits two numbers. The fix is to require the rule to reproduce all four.
Mistake: assuming addition. Players see 2, 4, 8 and answer 14 by adding +2, +4, +6. The pattern is actually ×2, so the answer is 16. The fix is to test the ratio as early as the differences.
Mistake: arithmetic slip in the final step. Recovering the rule correctly and then adding wrong is the most frustrating way to lose a point. The fix is to redo the last calculation rather than trusting it.
A short, honest FAQ
Do I need to install anything? No. It runs in any modern browser.
Is there always one right answer? In principle any list can be extended many ways; in practice every sequence here has an intended rule from the three families above, and the choices are built around it.
What age is it for? Roughly grades 5 and up, or any adult who enjoys pattern puzzles.