Puzzle 1
Which number comes next?
- 37
- 40
- 43
- 46
- 49
- ?
52
51
98
50
55
49
Show the answer
Answer: A
Why. Each number is 3 more than the one before: 37, 40, 43, 46, 49. Next: 49 + 3 = 52.
How to Solve Number Series Puzzles
A number series puzzle asks you to find the rule connecting its terms. Check differences first, then ratios, squares or cubes, and alternating terms. Test a possible rule against every term before choosing an answer.
Puzzle 2
Which number comes next?
- 8
- 12
- 16
- 20
- 24
- ?
272844382448Show the answer
Answer: B
Why. Each number is 4 more than the one before: 8, 12, 16, 20, 24. Next: 24 + 4 = 28.
Puzzle 3
Which number comes next?
- 2
- 6
- 18
- 54
- 162
- 486
- ?
9722430145814596484374Show the answer
Answer: C
Why. Each number is triple the one before: 2, 6, 18, 54, 162, 486. Next: 486 × 3 = 1458.
Puzzle 4
Which number comes next?
- 31
- 67
- 103
- 139
- 175
- 211
- ?
249211283247245422Show the answer
Answer: D
Why. Each number is 36 more than the one before: 31, 67, 103, 139, 175, 211. Next: 211 + 36 = 247.
Puzzle 5
Which number comes next?
- 17
- 8
- 22
- 16
- 27
- 24
- 32
- ?
345631403264Show the answer
Answer: E
Why. Two series are woven together. The 1st, 3rd, 5th... numbers go 17, 22, 27, 32 (+5 each time); the 2nd, 4th, 6th... go 8, 16, 24 (+8 each time). Number 8 belongs to the second series, so the next number is 32.
Puzzle 6
Which number comes next?
- 12
- 14
- 19
- 27
- 38
- 52
- ?
5489551047969Show the answer
Answer: F
Why. The gaps between neighbours are +2, +5, +8, +11, +14: each gap is 3 bigger than the one before. Next gap: +17, so 52 + 17 = 69.
Puzzle 7
Which number comes next?
- 1
- 5
- 6
- 11
- 17
- 28
- ?
455650326273Show the answer
Answer: A
Why. Each number is the sum of the two before it: 1, 5, 6, 11, 17, 28. Next: 17 + 28 = 45.
Puzzle 8
Which number comes next?
- 120
- 211
- 338
- 507
- 724
- ?
94199514489968151231Show the answer
Answer: B
Why. Each number is a cube minus 5: 5³ − 5 = 120, 6³ − 5 = 211, 7³ − 5 = 338, and so on. Next: 10³ − 5 = 995.
How should you start a number series?
Start by subtracting each term from the next to see whether the difference stays the same. If it does not, check whether each term is multiplied by the same amount.
If neither fits, look at how the differences change: they may move by a fixed step. You can also check whether terms match square or cube patterns, or whether each term comes from adding the two before it.
How can you spot an alternating rule?
An alternating series uses two rules in turn, one for terms in odd positions and another for terms in even positions. Write the two tracks separately and look for a simple pattern in each.
Cube patterns can also involve a fixed change between terms. Whatever rule you try, check that it accounts for every term, rather than fitting only the last pair.
What mistakes should you avoid?
A short series can fit more than one possible rule. Prefer a simple rule that explains the full sequence, and be cautious about a complicated explanation that accounts for only one gap.
This page has 8 puzzles with answers and explanations. Use each explanation to compare the proposed rule with the terms. For more practice, see all practice sets. The free timed test includes several reasoning formats, but it does not print an IQ score.
Questions
Should I check differences or ratios first?
Check differences first because a constant increase or decrease is easy to spot. If the gaps vary, check whether each term is multiplied by the same amount. Then consider changing gaps, powers, or a rule that uses earlier terms.
What if more than one rule fits the series?
Choose the simplest rule that fits every term shown. A few terms may allow several possible patterns, so avoid adding extra conditions without evidence. If answer choices are provided, check which choice works consistently across the sequence.
How do I solve an alternating number series?
Separate the terms into two tracks: odd-position terms in one track and even-position terms in the other. Look for a simple rule within each track, then verify that both rules explain all the terms.