1. The Chinese Football League A has 12 football clubs participating, with a home and away double round-robin system, meaning any two teams play each other twice, once at home and once away. A win earns 3 points, a draw earns 1 point each, and a loss earns 0 points. At the end of the league, teams are ranked according to their points. The maximum points difference between two teams with adjacent positions on the points table can be $\qquad$ points.
$=1.46$ points.
Suppose the score difference between the $k$-th and the $(k+1)$-th is the largest. Since the total score of each match between any two teams is at most 3 points and at least 2 points, the maximum total score of the first $k$ teams playing against each other is $3 \cdot 2 C_{k}^{2}=6 C_{k}^{2}$. Additionally, the maximum total score of the first $k$ teams playing against the remaining $12-k$ teams is $3 \cdot 2 k(12-\dot{k})$. Therefore, the maximum total score of the first $k$ teams is $6 C_{k}^{2}+6 k(12-k)$. Thus, the maximum score of the $k$-th team is $\frac{6 C_{k}^{2}+6 k(12-k)}{k}=69-3 k$ points.

The minimum total score of the remaining $12-k$ teams playing against each other is $2(12-k)(11-k)$ points. Therefore, the minimum score of the $(k+1)$-th team is $2(11-k)$ points.

Thus, the score difference between the $k$-th and the $(k+1)$-th team is $(69-3 k) - 2(11-k) = 47 - k$ points, and its maximum value is 46 points when $k=1$.

In fact, if the first team wins all 22 matches and scores 66 points, while the remaining 11 teams draw against each other and each scores 20 points, the difference is exactly 46 points.