To continue the sequence of tiles shown, the tile indicated by the question mark should be: (The tiles in the sequence contain, in order, 0 dots, 1 dot, 1 dot, 2 dots, 3 dots, and 5 dots, followed by a tile marked with a question mark.)
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Count the dots on each tile: 0, 1, 1, 2, 3, 5. This is the Fibonacci pattern, so the next tile needs 3 + 5 = 8 dots.
This question is a Fibonacci-style number pattern hidden inside pictures instead of numbers. Each tile carries a certain number of dots, and the job is to work out what number of dots the seventh tile should carry.
List the dot counts of the six visible tiles: $0, 1, 1, 2, 3, 5$. A well known number pattern called the Fibonacci sequence starts $0, 1, 1, 2, 3, 5, 8, 13, ...$, where from the third term onward, each number is the sum of the two numbers just before it. Comparing our six dot counts to this pattern shows they match term by term: $0, 1, 1, 2, 3, 5$ is exactly the start of the Fibonacci sequence.
Since the seventh Fibonacci number (right after $0, 1, 1, 2, 3, 5$) is $5 + 3 = 8$, the missing tile in the question must carry 8 dots.
Option (A), 4 dots: 4 does not equal $5+3$, so this tile does not continue the pattern.
Option (B), 6 dots: 6 also does not match the required sum of 8, so this is not the right tile either.
Option (C), 8 dots arranged in a ring: 8 matches $5+3$ exactly, so this is the tile that correctly continues the sequence.
Option (D), 9 dots: 9 is one more than the required 8, so this tile also fails to fit the pattern.
Let's summarize:
The dot counts 0, 1, 1, 2, 3, 5 follow the Fibonacci rule, where each term is the sum of the two terms before it.
The next term after 3 and 5 must be $3+5=8$.
Only the tile with 8 dots, option (C), matches this required count.
So the tile indicated by the question mark must show 8 dots, confirming option (C) as correct.
