Question:
Two tiles are missing in Panel I. Which one of the options in Panel II is the appropriate choice for the missing tiles?
Two tiles are missing in Panel I. Which one of the options in Panel II is the appropriate choice for the missing tiles?
Show Hint
Count the filled dots in each tile and look for a magic square pattern.
Updated On: Aug 17, 2026
- (i)
- (ii)
- (iii)
- (iv)
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The Correct Option is A
Solution and Explanation
Step 1: Count the filled dots in each known tile.
Each tile is a 3x3 grid of dots, filled or open, and Panel I arranges 9 such tiles in a 3x3 layout with the last two tiles, middle-right and bottom-right, missing.
Counting the filled dots in each of the 7 known tiles gives, row by row: 8, 1, 6 in row 1; 3, 5 in row 2; 4, 9 in row 3.
Step 2: Spot the number pattern.
The numbers 8, 1, 6 in row 1 add up to 15, and the numbers 4, 9 in row 3 already total 13 with one tile left to find.
These counts are exactly the digits 1 to 9 arranged as the classic 3x3 magic square, where every row, column and diagonal adds up to 15.
Step 3: Solve for the missing counts.
For row 2: \(3 + 5 + x = 15\), so \(x = 7\) filled dots in the middle-right tile.
For row 3: \(4 + 9 + y = 15\), so \(y = 2\) filled dots in the bottom-right tile.
Checking column 3: \(6 + 7 + 2 = 15\), which matches and confirms the pattern is consistent.
Step 4: Match against the options.
Each option in Panel II stacks two tiles, an upper tile for the middle-right position and a lower tile for the bottom-right position.
Only option (i) has an upper tile with exactly 7 filled dots and a lower tile with exactly 2 filled dots; the other options show 6 dots in the upper tile or a different count below.
Final Answer:
Option (i) supplies the missing tiles with dot counts 7 and 2, completing the magic square pattern. \[ \boxed{\text{Answer} = \text{(i)}} \]
Each tile is a 3x3 grid of dots, filled or open, and Panel I arranges 9 such tiles in a 3x3 layout with the last two tiles, middle-right and bottom-right, missing.
Counting the filled dots in each of the 7 known tiles gives, row by row: 8, 1, 6 in row 1; 3, 5 in row 2; 4, 9 in row 3.
Step 2: Spot the number pattern.
The numbers 8, 1, 6 in row 1 add up to 15, and the numbers 4, 9 in row 3 already total 13 with one tile left to find.
These counts are exactly the digits 1 to 9 arranged as the classic 3x3 magic square, where every row, column and diagonal adds up to 15.
Step 3: Solve for the missing counts.
For row 2: \(3 + 5 + x = 15\), so \(x = 7\) filled dots in the middle-right tile.
For row 3: \(4 + 9 + y = 15\), so \(y = 2\) filled dots in the bottom-right tile.
Checking column 3: \(6 + 7 + 2 = 15\), which matches and confirms the pattern is consistent.
Step 4: Match against the options.
Each option in Panel II stacks two tiles, an upper tile for the middle-right position and a lower tile for the bottom-right position.
Only option (i) has an upper tile with exactly 7 filled dots and a lower tile with exactly 2 filled dots; the other options show 6 dots in the upper tile or a different count below.
Final Answer:
Option (i) supplies the missing tiles with dot counts 7 and 2, completing the magic square pattern. \[ \boxed{\text{Answer} = \text{(i)}} \]
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