IMO Practice Test — Patterns
6 Questions • 15 min • Olympiad level
15:00
Question 1 of 6
A pattern starts: 2, 5, 3, 6, 4, 7, 5, 8, ___. What is the next number?
6
9
10
4
Explanation: Two interleaved patterns: +3,+3,+3... (2,5,3? Wait 2→5=+3, 5→3=-2, 3→6=+3, 6→4=-2, 4→7=+3, 7→5=-2, 5→8=+3, 8→? = -2 = 6
Question 2 of 6
How many triangles are in the 10th position of this pattern? Pattern: ▲, ▲▲, ▲▲▲, ▲▲▲▲, ...
9
10
11
12
Explanation: Growing pattern: position n has n triangles. 10th position has 10 triangles
Question 3 of 6
A colour pattern uses 4 colours: R, B, G, Y in that order. If the pattern has 50 colours, how many complete cycles are there? What colour is the 47th?
12 cycles, G
12 cycles, B
12 cycles, Y
12 cycles, R
Explanation: Core length 4. 50÷4=12 remainder 2. 12 complete cycles. 47th: 47÷4=11 remainder 3. Remainder 3 = 3rd colour = B
Question 4 of 6
Complete this pattern: 1, 1, 2, 3, 5, 8, ___, 21
11
12
13
14
Explanation: Fibonacci pattern: each number is sum of previous two. 5+8=13
Question 5 of 6
A pattern is made by writing numbers: 1, 11, 21, 1211, 111221, ___. This is the "look and say" sequence. What is the next?
312211
312221
311221
312231
Explanation: Each term describes previous: 111221 → three 1s, two 2s, one 1 = 312211
Question 6 of 6
In a repeating pattern, the 1st shape is ▲, 8th shape is ●, 15th shape is ■. What is the core length?
5
6
7
8
Explanation: Positions 1,8,15 are in same position in core. Difference 7. Core length divides 7. 1,8,15 differ by 7, so core length must be 7