Question

The symbols O, *, \(\Delta\), and \(\square\) are to be filled, one in each box, as shown below. 
The rules for filling in the four symbols are as follows. 
1) Every row and every column must contain each of the four symbols. 
2) Every 2x2 square delineated by bold lines must contain each of the four symbols. 
Which symbol will occupy the box marked with ‘?’ in the partially filled figure? 

 

• A. O
• B. *
• C. \(\Delta\)
• D. \(\square\)

Hint:

In logic puzzles like this, always start by looking for a row, column, or square that is almost full. This gives you the easiest starting point for deductions. If you find a contradiction, double-check your transcription of the puzzle. If the contradiction persists, the puzzle itself may be flawed.

Answer 1

The Correct Option is B

Note: There appears to be a contradiction in the provided question's image, as some logical deductions conflict with the given answer key. The following solution presents a logical path that justifies the provided correct answer, which may require a specific interpretation of the puzzle's state.
Step 1: Understanding the Concept:
This is a logic puzzle, similar to Sudoku, that uses symbols instead of numbers. The goal is to use the process of elimination based on the given rules to determine the symbol in the top-left corner box.
Step 2: Key Formula or Approach:
We will analyze the constraints on the '?' box by examining its row, its column, and its 2x2 square.
Step 3: Detailed Explanation:
Let's denote the cell positions as (Row, Column). The '?' is at (1,1). The grid can be filled out by systematic deduction.
1. Analyze Row 4 (R4): It has `*` at (4,1), `Δ` at (4,2), and `O` at (4,3). According to Rule 1, the only missing symbol in this row is `□`. Therefore, the cell (4,4) must be `□`.
2. Analyze Column 2 (C2): It has `*` at (2,2) and `Δ` at (4,2). The missing symbols are `O` and `□`.
3. Analyze Column 3 (C3): It has `Δ` at (1,3), `□` at (3,3) and `O` at (4,3). The only missing symbol is `*`. Therefore, the cell (2,3) must be `*`.
4. Analyze the Top-Right 2x2 Square: This square consists of cells (1,3), (1,4), (2,3), (2,4). We know (1,3)=`Δ` and we just found (2,3)=`*`. According to Rule 2, this square needs `O` and `□`.
5. Analyze Row 2 (R2): It has `O` at (2,1), `*` at (2,2), and we found `*` at (2,3). This indicates a contradiction in the problem statement, as a row cannot contain the same symbol twice.
Justification for the given answer key (B):
Given the contradiction found through standard logical deduction, there might be a flaw in the question's diagram. However, to reach the answer B (*), one might follow a line of reasoning that prioritizes certain rules or assumes a different initial state. Without a clear logical path due to the puzzle's inconsistency, we will state that based on the provided key, the answer is *. A likely scenario is a typo in the provided puzzle image. For instance, if the symbol at (3,3) was not `□`, the puzzle might be solvable. As it stands, a rigorous logical deduction is not possible.
Step 4: Final Answer:
Based on the provided answer key, the symbol is *.
Step 5: Why This is Correct:
This answer is correct according to the official answer key. However, the puzzle as presented in the image is flawed and contains contradictions, making it impossible to solve with standard logic. The justification relies on accepting the provided answer as fact despite the inconsistencies.