IMO Practice Test — Patterns
6 Questions • 12 min • Olympiad level
12:00
Question 1 of 6
hard
Find the missing number: 2, 4, 8, 16, __
18
24
32
20
Explanation: Rule ×2 → 32.
Question 2 of 6
hard
1, 4, 9, 16, __ (square numbers)
20
24
25
30
Explanation: 1,4,9,16,25 are 1×1,2×2,3×3,4×4,5×5.
Question 3 of 6
hard
What is the 6th term: 3, 6, 9, 12, …?
15
18
21
24
Explanation: Rule +3: 3,6,9,12,15,18 → 6th is 18.
Question 4 of 6
hard
Pattern: 1, 1, 2, 3, 5, 8, __ (add the last two)
11
12
13
10
Explanation: 5 + 8 = 13 (Fibonacci).
Question 5 of 6
medium
Continue: 50, 45, 40, 35, __?
25
30
32
20
Explanation: Rule −5 → 30.
Question 6 of 6
hard
In 🔺🔺🔵🔺🔺🔵…, what is the 9th shape?
🔺
🔵
⭐
🔴
Explanation: The group 🔺🔺🔵 repeats every 3. Positions 7, 8, 9 are 🔺, 🔺, 🔵 — so the 9th shape is 🔵.