How does the number sequence test work?
Each puzzle shows a line of numbers that follow one rule. Work out the rule and pick the next number from 4 choices. There are 10 sequences: the first five use simpler rules (adding or multiplying by the same amount, square numbers and gaps that grow), the last five trickier ones such as Fibonacci-style sums, two sequences taking turns, cube numbers and primes.
Your result is how many you got right, with your time over the whole set. After each answer the rule is explained, so a wrong answer still shows you the pattern.
Is there only one right answer?
Within the rules this test uses, yes. Strictly, any list of numbers can be continued in endless ways: whatever next number you choose, some formula passes through the numbers shown and that one. So every puzzle is checked against all the rules the test knows, and kept only if every rule that fits agrees on the next number and no wrong choice fits any rule.
What rules appear in number sequences?
These nine, one example each. The site's tests check each example has a single answer under the same rules.
| Rule | Example | Next |
|---|---|---|
| Add the same amount each time | 3, 7, 11, 15, 19 | 23 |
| Multiply by the same number | 2, 6, 18, 54, 162 | 486 |
| Square numbers | 4, 9, 16, 25, 36 | 49 |
| Gaps that grow by the same amount | 1, 3, 7, 13, 21 | 31 |
| Add the two numbers before (Fibonacci-style) | 2, 3, 5, 8, 13 | 21 |
| Two sequences taking turns | 3, 30, 6, 28, 9, 26 | 12 |
| Add, then double, in turn | 2, 5, 10, 13, 26 | 29 |
| Cube numbers | 1, 8, 27, 64, 125 | 216 |
| Prime numbers | 2, 3, 5, 7, 11 | 13 |
The Fibonacci rule is named after Leonardo of Pisa, known as Fibonacci, whose 1202 book Liber Abaci used it in a puzzle about breeding rabbits.
How do you find the rule?
- Look at the gaps. Write the difference between each pair. Equal gaps mean adding; gaps that grow evenly mean the gaps themselves follow a rule.
- Try dividing. If the numbers grow fast, each may be the one before times the same number.
- Skip one. If the numbers go up and down, read every other one: there may be two sequences taking turns.
- Know the famous ones. Squares (1, 4, 9, 16), cubes (1, 8, 27, 64) and primes (2, 3, 5, 7, 11) are worth recognising on sight.
For patterns in pictures rather than numbers, try Matrix Reasoning; for quick sums against the clock, the Mental Math Test.