1. **Stating the problem:** We have four large squares arranged in a 2x2 grid. Each large square contains four numbers arranged in a 2x2 pattern. The bottom-right square has a missing number represented by "?". We need to find this missing number. 2. **Observing the pattern:** Each large square has four numbers: top-left, top-right, bottom-left, and bottom-right. The inner smaller square inside each large square contains a number that appears to be related to the four numbers in that square. 3. **Analyzing the given data:** - Top-left square: numbers are 7, 12, 15, 7; inner number is 7. - Top-right square: numbers are 11, 16, 3, 3; inner number is 3. - Bottom-left square: numbers are 9, 7, 8, 17; inner number is 7. - Bottom-right square: numbers are ?, 15, 21, 6; inner number is ? (unknown). 4. **Hypothesis:** The inner number might be the greatest common divisor (GCD) of the four numbers in the large square. 5. **Check the hypothesis:** - For top-left: GCD(7, 12, 15, 7) = 1, but inner number is 7, so this does not fit. - For top-right: GCD(11, 16, 3, 3) = 1, inner number is 3, no match. 6. **Try another approach:** The inner number might be the minimum number among the four numbers. - Top-left: min(7, 12, 15, 7) = 7, inner number is 7, matches. - Top-right: min(11, 16, 3, 3) = 3, inner number is 3, matches. - Bottom-left: min(9, 7, 8, 17) = 7, inner number is 7, matches. 7. **Conclusion:** The inner number is the minimum of the four numbers in the large square. 8. **Find the missing number:** For bottom-right square, inner number is unknown, but the other three numbers are 15, 21, and 6. Since the inner number is the minimum of the four numbers, and the inner number is unknown, but the question mark is in the top-left position, we can find the missing number by setting the minimum equal to the inner number. 9. **Assuming the inner number is the minimum of the four numbers:** - The known numbers are 15, 21, 6. - The minimum of these three is 6. 10. **Therefore, the missing number must be greater than or equal to 6 to keep 6 as the minimum. But since the inner number is unknown, and the question mark is the missing number, the inner number is the minimum of the four numbers including the missing one. So the missing number must be at least 6 or more to keep 6 as the minimum. But if the missing number is less than 6, then the inner number would be that missing number. 11. **Since the inner number is unknown, but the pattern suggests the inner number is the minimum, and the inner number is the question mark, the missing number is the inner number. So the missing number is the minimum of the four numbers. The minimum of 15, 21, 6, and ? is ?. 12. **To keep the pattern consistent, the missing number must be less than or equal to 6 to be the minimum. Since 6 is the smallest known number, the missing number must be less than or equal to 6. The only number that fits the pattern is 6 itself, which is already present. 13. **Therefore, the missing number is 6.** **Final answer:** The missing number is $6$.