Question

To continue the sequence of tiles shown, the tile indicated by the question mark should be:

• A.

  

• B.

  

• C.

  

• D.

  

Hint:

Count the dots on each tile: 0, 1, 1, 2, 3, 5. Check if each number is the sum of the two before it (the Fibonacci rule) and use that to find the missing count.

Answer 1

The Correct Option is C

Step 1: Count the dots on each tile in the sequence.
Reading the seven tiles from left to right and counting the black dots on each one gives the counts
\[ 0,\ 1,\ 1,\ 2,\ 3,\ 5,\ ? \]

Step 2: Look for a pattern in these counts.
Check whether each count is the sum of the two counts right before it:
\[ 0+1=1,\quad 1+1=2,\quad 1+2=3,\quad 2+3=5 \]
Every number in the list is exactly the sum of the previous two numbers. This is the Fibonacci pattern.

Step 3: Use the pattern to find the missing count.
Following the same rule, the seventh tile should carry
\[ 3+5=8 \]
dots.

Step 4: Match this count to the given options.

(A): Shows a tile with 4 dots arranged in a 2 by 2 block. This does not match 8, so it is incorrect.

(B): Shows a tile with 6 dots. This does not match 8 either, so it is incorrect.

(C): Shows a tile with 8 dots. This matches the required count, so it is the correct choice.

(D): Shows a tile with 9 dots. One too many compared to the required 8, so it is incorrect.

Final Answer:
The number of dots follows the Fibonacci sequence 0, 1, 1, 2, 3, 5, 8, so the missing tile must carry 8 dots.
\[ \boxed{\text{Tile with 8 dots, option (C)}} \]