In the provided image, you are asked to find the missing value in the 3x3 grid. The grid contains the following numbers:

84   18
79   -9
54   ?
66   0

You are given options to choose from: 1, -1, 9, or none of these.

Let's analyze the grid:

1. In many puzzles like this, patterns occur in either rows, columns, or diagonals. One common strategy is to check for arithmetic patterns, differences, or ratios in the numbers.

Row by Row Pattern:

1. First row:

   • $84 - 18 = 66$ (Difference between first and second columns in the first row)

2. Second row:

   • $79 - (-9) = 88$, which doesn’t fit a simple progression with the first row's difference.

3. Third row:

   • $54 - ? = 66$, suggests the pattern might not be column-based directly.

Investigating Columns:

• First Column: The numbers decrease by 5 in each row (from 84 to 79 to 54, then to 66).
• Second Column: Let's check for a pattern between the second column values: 18, -9, and ?. The difference between 18 and -9 is -27. Continuing this pattern, the difference between -9 and the next value should also be -27. Therefore, $-9 - 27 = -36$.

Conclusion:

The missing value is -36, but this is not an option. Therefore, the answer is "None of these".

Would you like further clarification or details?

Follow-up questions:

1. How can we systematically identify patterns in number grids?
2. What are other common strategies for solving grid puzzles?
3. How does this puzzle compare to Sudoku in terms of logic?
4. Can this method of arithmetic sequences apply to different grid sizes?
5. Are there other possible patterns (e.g., geometric) that could work?

Tip: When working with number puzzles, always look for simple arithmetic or geometric progressions first.