【Solution】Solution: Since the number of layers and the number of points per layer are integers, and the numbers of each layer form an arithmetic sequence with a common difference of 1.

If the number of layers is odd, the total number $=$ number of layers $\times$ number of points in the middle layer.
Since the total number 2014 is even,
the number of points in the middle layer must be even, divided into: $a$ (middle layer point number 2, number of layers 1007), $b$ (middle layer point number 38, number of layers 53), $c$ (middle layer point number 106, number of layers 19).
In case $a$, the number of points in the layers before the middle layer becomes negative, and after verification, cases $b$ and $c$ are reasonable.
If the number of layers is even, because the common difference of the sequence is 1, the sum of the points in the two middle layers must be odd,
divided into: $d$ (sum of points in the two middle layers 19, number of layers 212), $e$ (sum of points in the two middle layers 53, number of layers 76), $f$ (sum of points in the two middle layers 1007, number of layers 4), in which $212=2 \times 53 \times 2$,

Similarly: in cases $e$ and $f$, the number of layers can be derived similarly. Similar to when the number of layers is odd, verification shows that case $f$ is reasonable.
Therefore, there are 3 different methods.
So the answer is: $A$.
11. (10 points) As shown in the figure, 15 points can be arranged into a triangular array or a trapezoidal array in 3 different ways (rule: the number of points in adjacent rows differs by 1). Therefore, the number of different ways to arrange 2014 points into a triangular array or a trapezoidal array (at least two layers) is ( ).
A. 3
B. 7
C. 4
D. 9