Discussion
To continue the sequence of tiles shown, the tile indicated by the question mark should be
(The figure shows a row of square tiles holding, in order, 0, 1, 1, 2, 3 and 5 dots, followed by a dashed tile marked ?.)
Answer: C
The missing tile is the tile with 8 dots.
The tiles hold 0, 1, 1, 2, 3 and 5 dots. From the third tile on, each count is the sum of the two before it, which is the Fibonacci sequence:
\[ \begin{aligned} 0 + 1 &= 1, \quad 1 + 1 = 2, \quad 1 + 2 = 3 \\ 2 + 3 &= 5, \quad 3 + 5 = 8 \end{aligned} \]
So the next tile must carry 8 dots. The tiles with 4 and 6 dots fall short, and the 3 by 3 tile with 9 dots is one too many; a simple 'add one more dot' or 'square number' rule does not fit the counts already shown.
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