Correct Answer :
Solution :
The correct answer is the star symbol (★).
To find the symbol that occupies the box marked with '?', we can solve the grid step-by-step using the two given rules:
1. Every row and every column must contain each of the four symbols: circle (○), star (★), triangle (Δ), and square (□).
2. Every 2×2 square delineated by bold lines must contain each of the four symbols.
Step 1: Fill the missing symbol in Row 4
Looking at the bottom row (Row 4):
- The first cell contains the star (★).
- The third cell contains the triangle (Δ).
- The fourth cell contains the circle (○).
Since every row must contain all four symbols, the only remaining symbol for the second cell in Row 4 is the square (□).
Therefore, the cell at (Row 4, Column 2) = □.
Step 2: Determine the possibilities for Column 2
Looking at Column 2 from top to bottom:
- The first cell is marked with '?'.
- The second cell contains the circle (○).
- The fourth cell contains the square (□).
Since Column 2 must contain all four symbols, the remaining two cells—the cell marked with '?' at (Row 1, Column 2) and the empty cell at (Row 3, Column 2)—must be filled by the star (★) and the triangle (Δ).
This gives us our first constraint:
? ∈ {★, Δ}
Step 3: Analyze the Top-Right 2×2 Block and Row 1
Let us find the symbol for the cell at (Row 1, Column 3):
- The top-right 2×2 block contains the cells (Row 1, Column 3), (Row 1, Column 4) = Δ, (Row 2, Column 3) = ★, and (Row 2, Column 4).
- Row 2 already contains the circle (○) at (Row 2, Column 2), so the cell at (Row 2, Column 4) cannot be a circle.
- Therefore, within the top-right 2×2 block, the circle (○) must occupy the cell at (Row 1, Column 3).
Now, looking at Row 1:
- The third cell contains the circle (○).
- The fourth cell contains the triangle (Δ).
Since Row 1 must contain all four symbols, the remaining two cells—(Row 1, Column 1) and the cell marked with '?' at (Row 1, Column 2)—must be filled by the star (★) and the square (□).
This gives us our second constraint:
? ∈ {★, □}
Step 4: Find the intersection of the two constraints
Comparing the two constraints for the cell marked with '?':
- From Column 2, ? must be either ★ or Δ.
- From Row 1, ? must be either ★ or □.
The only symbol that satisfies both constraints is the star (★).
Therefore, the box marked with '?' must be occupied by the star symbol (★).
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