1. The problem involves finding the number associated with the first triangle in the top-left corner, which contains the numbers 10, 2, 8, and 1, and is linked to the circle number 9. 2. To solve this, we need to identify a pattern or rule that relates the four numbers inside the triangle to the number in the circle. 3. Let's analyze the numbers: 10, 2, 8, 1. 4. One possible approach is to sum the numbers: $10 + 2 + 8 + 1 = 21$. 5. The circle number is 9, which is less than 21, so maybe the circle number is related to the sum in another way. 6. Another approach is to consider the difference between the largest and smallest numbers: $10 - 1 = 9$. 7. This matches the circle number 9 exactly. 8. Therefore, the pattern is that the circle number equals the difference between the largest and smallest numbers inside the triangle. 9. This rule can be expressed as: $$\text{Circle number} = \max(a,b,c,d) - \min(a,b,c,d)$$ where $a,b,c,d$ are the numbers inside the triangle. 10. Applying this to the first triangle: $$\max(10,2,8,1) - \min(10,2,8,1) = 10 - 1 = 9$$ which matches the given circle number. Final answer: The circle number 9 is the difference between the largest and smallest numbers inside the triangle.