1. **Stating the problem:** We have three bracketed numbers arranged in a pattern with numbers before, after, above, and below each bracketed number. The first two bracketed numbers are given: 25 and 9. The third bracketed number is unknown (?). We need to find the value of this unknown bracketed number. 2. **Analyzing the first bracketed number (25):** - Numbers around it: before = 9, after = 4, above = 12, below = 7 - Check if the bracketed number relates to these numbers by a pattern. - Try sum of above and below: $12 + 7 = 19$ - Try sum of before and after: $9 + 4 = 13$ - Try product of above and below: $12 \times 7 = 84$ - Try product of before and after: $9 \times 4 = 36$ - Try sum of all four: $9 + 4 + 12 + 7 = 32$ - Try difference or other operations: - $12 \times 7 - (9 + 4) = 84 - 13 = 71$ (no) - $9 \times 4 - (12 + 7) = 36 - 19 = 17$ (no) - Try sum of squares of before and after: $9^2 + 4^2 = 81 + 16 = 97$ (no) - Try sum of squares of above and below: $12^2 + 7^2 = 144 + 49 = 193$ (no) - Try difference of squares of above and below: $12^2 - 7^2 = 144 - 49 = 95$ (no) - Try difference of squares of before and after: $9^2 - 4^2 = 81 - 16 = 65$ (no) - Try product of before and after minus product of above and below: $9 \times 4 - 12 \times 7 = 36 - 84 = -48$ (no) - Try sum of before and after multiplied by sum of above and below: $(9 + 4) \times (12 + 7) = 13 \times 19 = 247$ (no) - Try sum of before and after multiplied by difference of above and below: $(9 + 4) \times (12 - 7) = 13 \times 5 = 65$ (no) - Try difference of before and after multiplied by sum of above and below: $(9 - 4) \times (12 + 7) = 5 \times 19 = 95$ (no) - Try difference of before and after multiplied by difference of above and below: $(9 - 4) \times (12 - 7) = 5 \times 5 = 25$ (yes!) 3. **Confirming the pattern:** - The bracketed number equals $(\text{before} - \text{after}) \times (\text{above} - \text{below})$ - For the first bracket: $(9 - 4) \times (12 - 7) = 5 \times 5 = 25$ 4. **Check the second bracketed number (9):** - Numbers: before = 14, after = 11, above = 5, below = 2 - Calculate: $(14 - 11) \times (5 - 2) = 3 \times 3 = 9$ - Matches the given bracketed number. 5. **Find the unknown bracketed number (?):** - Numbers: before = 8, after = 3, above = 6, below = 4 - Calculate: $(8 - 3) \times (6 - 4) = 5 \times 2 = 10$ **Final answer:** The unknown bracketed number is $10$.