Write the dot count separately for each quadrant. Check whether the third count equals the first count plus the missing count in every corresponding quadrant.
Step 1: Observe that each figure is a \(2 \times 2\) grid with dots placed in each quadrant.
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Step 2: Compare the given grids from left to right. The pattern shows that:
\begin{itemize}
\item The total number of dots increases in a systematic way,
\item The distribution of dots across the four quadrants follows a consistent rearrangement rule,
\item Corresponding quadrants across successive figures change in a predictable manner.
\end{itemize}
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Step 3: Using the two completed examples on the right as references, infer the missing grid such that:
\begin{itemize}
\item The dot count in each quadrant aligns with the progression,
\item The overall balance and symmetry of dots matches the sequence.
\end{itemize}
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Step 4: Checking all options:
\begin{itemize}
\item Options A, B, D: Violate either the dot-count progression or quadrant-wise distribution.
\item C: Satisfies both the numerical progression and positional pattern — correct.
\end{itemize}
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Final Answer:
\[
\boxed{C}
\]
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Approach Solution -2
Concept:
Treat each quadrant as its own number sequence.
In every quadrant, the dot count in the next grid is the sum of the counts in the previous two grids.
Step 1: Record the first and third grids.
In the order top-left, top-right, bottom-left, bottom-right, the first grid has counts $(2,1,0,1)$.
The third grid has counts $(5,4,1,2)$.
Step 2: Recover the missing grid by subtraction.
For each matching quadrant, missing count equals third-grid count minus first-grid count.
$(5-2,4-1,1-0,2-1)=(3,3,1,1)$
Step 3: Check the continuation.
Adding the missing grid to the third grid gives the fourth counts quadrant by quadrant, following the same sum rule.
Thus the missing grid must contain $3,3,1,1$ dots in its four quadrants.
Step 4: Match the count pattern with the options.
Only option C has three dots in each upper quadrant and one dot in each lower quadrant.
Final Answer: Option C.
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