10. (12 points) Fill 4 out of the 6 digits from $0-5$ into the circles in Figure 1. The difference between the numbers at the ends of each line segment can be calculated, resulting in 5 differences, which are exactly $1-5$. Figure 2 shows one possible arrangement. How many arrangements meet the requirement? (In the figure, swapping 3 and 5 or 0 and 1 counts as a new arrangement.)

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10. (12 points) Fill 4 out of the 6 digits from $0-5$ into the circles in Figure 1. The difference between the numbers at the ends of each line segment can be calculated, resulting in 5 differences, which are exactly $1-5$. Figure 2 shows one possible arrangement. How many arrangements meet the requirement? (In the figure, swapping 3 and 5 or 0 and 1 counts as a new arrangement.)
【Solution】Solution: Select 4 numbers from the 6 numbers $0-5$, and take the difference between each pair. If the differences are exactly $1-5$, then the 4 selected numbers must include 0 and 5, and there are four ways to choose the four numbers: $0,5,1,3$, $0,5,1,2$, $0,5,2,4$, $0,5,3,4$. In each selection, there are always two pairs with the same difference, for example, $5-3=3-1$, so $(5,3)(3,1)$ cannot be connected at the same time. According to this, classify: $A, D$ are filled with $(5,3)(3,1)$, each having $2 \times 2=4$ ways to fill, for a total of 8 ways to fill. In summary, the four ways to select the numbers have $4 \times 8=32$ ways to fill, so the answer is 32.