12.1
3.
1
1,	2
1,	3
1,	2,	4
1,	2,	4,	8, 16
1,	3,	7,	15, 30
1,	3,	6,	12, 25, 50, 100
4.
113
140, 70
168, 84, 42
120, 60, 30
160, 80, 40, 20, 10
5.
*
[*]
([*])
([([*])])
[([([*])])]
12.2
8.
 call stack is the structure of information about all methods that have currently been called by your program. Recursion produces a tall call stack in which each recursive call is represented.
9. lines would stay in the original order
10.No base case so it would call its self forever
12.3
13.
6
4
7
0
1
14.
57
1029
-74
2438
132483
15.
7
6
4
10
5
20.
A image that recursively redraws smaller versions within itself
21.
public static void drawHexagon(Graphics g, Point position, int size) {
    Polygon poly = new Polygon();
    poly.addPoint(position.x, position.y + size / 2);
    poly.addPoint(position.x + size / 3, position.y);
    poly.addPoint(position.x + 2 * size / 3, position.y);
    poly.addPoint(position.x + size, position.y + size / 2);
    poly.addPoint(position.x + 2 * size / 3, position.y + size);
    poly.addPoint(position.x + size / 3, position.y + size);
    g.drawPolygon(poly);
}
22.
Recursion is an effective way to implement a backtracking algorithm because the memory of decisions and points to go back to are represented by the recursive call stack. The pattern of "choose, explore, un-choose is elegantly represented by recursive calls for each individual choice.
23.
A decision tree is a description of the set of choices that can be made by a recursive backtracking method at any point in the algorithm.
25.
moves: NE N
moves: N NE
moves: N N E
moves: N E N
moves: E N N