Olympiad topic · P1–P4
Number patterns
Number patterns are common in the Hua Xia Cup's P1 to P3 papers; harder ones skip terms or ask for a term far along.
Try one
★★ Medium1, 2, 4, 7, 11, ?
These numbers follow a pattern. What number goes in place of the ?
- Hint 1: Write down the gaps between neighbours. What pattern do the gaps follow?
- Hint 2: Each gap is 1 more than the last. What was the last gap, and so the next?
- 1.The gaps are 1, 2, 3, 4, growing by 1.
- 2.The next gap is 5: ? = 11 + 5 = 16.
Answer: 16
Four levels, step by step
- ★EasyFreeUnlimited questionsThe same amount added or taken each time.
- ★★MediumFreeUnlimited questionsChanging gaps, square numbers.
- ★★★HardFreeUnlimited questionsTwo rows taking turns, the nth number of a grouped pattern.
- ★★★★Expert (competition level)VIPUnlimited questionsSumming a list whose gaps double, a long sum of two rows taking turns, how many of 1, 3, 6, 10, … are multiples of a number.
Number patterns: what it is and how to solve it
A row of numbers follows a rule: find it, and the next or the nth number.
For example: 9, 12, 16, 21, 27, ? The gaps are 3, 4, 5, 6, so the next gap is 7: 27 + 7 = 34.
The key idea: Look at the gaps (or ratios) between neighbours; the gaps can have a rule of their own. If the numbers jump up and down, split the odd and even places; watch for square numbers and repeating groups too.
Practise this topic free →Easy to Hard (★ to ★★★) all free, unlimited questions, no download