1. **Stating the problem:** We have pairs of U-shaped figures divided into six sections each, with numbers in each section. The goal is to find the number in the middle circle of each U-shaped figure based on the numbers in the sections. 2. **Observing the samples:** - For the first top-left shape, the sections are 6, 7, 3, 0, 10, 6 and the middle circle is 16. - For the top-right shape, the sections are 5, 5, 2, 3, 10, 5 and the middle circle is 15. 3. **Hypothesis:** The middle circle number seems related to the sum of the numbers in the sections. Let's check the sums: - Top-left sum: $6 + 7 + 3 + 0 + 10 + 6 = 32$ - Middle circle: 16, which is half of 32. - Top-right sum: $5 + 5 + 2 + 3 + 10 + 5 = 30$ - Middle circle: 15, which is half of 30. 4. **Rule:** The middle circle number is half the sum of the six section numbers. 5. **Applying the rule to exercises 6 to 9:** - Exercise 6: - Left figure sections: 8, 4, 2, 6, 6, 6 - Sum: $8 + 4 + 2 + 6 + 6 + 6 = 32$ - Middle circle: $\frac{32}{2} = 16$ - Right figure sections: 2, 2, 6, 6, 4, 4 - Sum: $2 + 2 + 6 + 6 + 4 + 4 = 24$ - Middle circle: $\frac{24}{2} = 12$ - Exercise 7: - Left figure sections: 2, 10, 2, 10, 8, 8 - Sum: $2 + 10 + 2 + 10 + 8 + 8 = 40$ - Middle circle: $\frac{40}{2} = 20$ - Right figure sections: 3, 4, 6, 3, 4, 8 - Sum: $3 + 4 + 6 + 3 + 4 + 8 = 28$ - Middle circle: $\frac{28}{2} = 14$ - Exercise 8: - Left figure sections: 7, 9, 2, 8, 5, 9 - Sum: $7 + 9 + 2 + 8 + 5 + 9 = 40$ - Middle circle: $\frac{40}{2} = 20$ - Right figure sections: 4, 6, 4, 6, 2, 4 - Sum: $4 + 6 + 4 + 6 + 2 + 4 = 26$ - Middle circle: $\frac{26}{2} = 13$ - Exercise 9: - Left figure sections: 3, 6, 3, 4, 2, 6 - Sum: $3 + 6 + 3 + 4 + 2 + 6 = 24$ - Middle circle: $\frac{24}{2} = 12$ - Right figure sections: 2, 9, 1, 2, 6, 5 - Sum: $2 + 9 + 1 + 2 + 6 + 5 = 25$ - Middle circle: $\frac{25}{2} = 12.5$ 6. **Conclusion:** The middle circle number is half the sum of the six section numbers. For exercise 9 right figure, the middle circle is 12.5. **Final answers:** - Exercise 6: Left = 16, Right = 12 - Exercise 7: Left = 20, Right = 14 - Exercise 8: Left = 20, Right = 13 - Exercise 9: Left = 12, Right = 12.5