21 replies to this topic

[Molly Mae]

I hope I'm not stepping on any toes here, but I had a lot of fun with Super's and Ed's Racing puzzles. Next comes Hyperspace Racing. =P

This is a variant on Superprismatic's Cartesian Racing challenge and Captain Ed's Cartesian Boat Racing variation. The movement rules are the same, but include a 3rd dimension. In Super's challenge, you had to land on a series of marks in sequence; in Capt Ed's, the goal was to round a mark; in this challenge, you have to navigate through four spherical rings of radius 1 in any direction and in any order.

Goal: Move your spaceship around the course, navigate through all four spheres, and return to base (origin) in the minimum number of moves.

Movement: Your boat begins at the origin (0,0,0), with a velocity vector of (0,0,0).
Before each move, you specify an acceleration vector (a,b,c), where a, b, and c can independently take on integer values from the set (-1, 0, 1).
The move consists of: (a) update the velocity by adding the acceleration, and then (b) move the spaceship by the velocity vector.

Example: if the prior location was (10,11,12), and the prior velocity was (2,5,6), and you choose the acceleration vector (1,-1,0),
the new velocity becomes (3,4,6) and the new location becomes (13,15,18).

Course constraints: The course consists of an unordered series of four rings. A ring is a sphere of radius 1 with centers at the points provided below. Crossing through a sphere means passing through the center or any of the 6 adjacent points. Assume the course is "infinite", that is, from (-100,-100,-100) to (100,100,100)

Your path through the course must contain a move through each of the four rings in any order and in any direction.
The first ring is (-22,18,19)
The second sphere is (12,-12,26)
The third sphere is (38,-13, 0)
The fourth sphere is (-9,30,-18)
Return to base (origin)

[CaptainEd]

Lovely! "Passing through" a sphere means which?:
(a) a move ends on a sphere center or one of its 6 neighbors
(b) at least one of those 7 points lies on the line segment of a move
© something more complicated about the line and the volume surrounding the sphere center...
(d) other

Also, it appears that the origin itself is the 5th mark, and presumably is to be passed through in the same way?

What fun!

[Molly Mae]

Lovely! "Passing through" a sphere means which?:
(a) a move ends on a sphere center or one of its 6 neighbors
(b) at least one of those 7 points lies on the line segment of a move
© something more complicated about the line and the volume surrounding the sphere center...
(d) other

Also, it appears that the origin itself is the 5th mark, and presumably is to be passed through in the same way?

What fun!

For simplicity, the line segment must pass through the minimum and maximum of each axis (so I guess it's actually a cube and not a sphere). For instance, if the center of a ring is (1,5,9), the line must pass within 1 of each axis. Examples: (2,6,8), (0,6,10), and (1,4,9) would pass through that goal. (1,5,7) would not.

As for the origin: it must be your last stop. Starting there doesn't count. =P I guess I forgot to mention that the teleportation device is located at origin--it puts you there and takes you out when you're done.

[CaptainEd]

Spoiler for my first crack: 46 moves, way suboptimal

First off, I hit the sphere centers exactly, and I hit them at the end of the move, and I have no idea what the optimal sequence of spheres is.
0 0 0
-1 1 1
-3 3 2
-6 6 4
-10 9 7
-15 13 11
-19 16 15
-22 18 19 <==
-24 21 22
-25 25 24
-25 28 25
-24 30 25
-22 31 24
-19 32 23
-15 32 21
-12 31 19
-9 30 18 <==
-5 28 17
-1 25 16
2 21 15
4 17 15
5 13 16
5 9 18
6 5 21
6 1 24
7 -3 26
9 -7 27
10 -10 27
12 -12 26 <==
15 -13 24
19 -13 21
24 -13 17
29 -13 12
33 -13 8
36 -13 4
38 -13 0 <==
39 -12 -3
39 -10 -5
38 -7 -6
36 -5 -6
33 -4 -5
29 -3 -3
24 -2 -2
18 -1 -1
11 0 0
5 0 0
0 0 0

[Molly Mae]

Spoiler for my first crack: 46 moves, way suboptimal

First off, I hit the sphere centers exactly, and I hit them at the end of the move, and I have no idea what the optimal sequence of spheres is. 0 0 0 -1 1 1 -3 3 2 -6 6 4 -10 9 7 -15 13 11 -19 16 15 -22 18 19 <== -24 21 22 -25 25 24 -25 28 25 -24 30 25 -22 31 24 -19 32 23 -15 32 21 -12 31 19 -9 30 18 <== -5 28 17 -1 25 16 2 21 15 4 17 15 5 13 16 5 9 18 6 5 21 6 1 24 7 -3 26 9 -7 27 10 -10 27 12 -12 26 <== 15 -13 24 19 -13 21 24 -13 17 29 -13 12 33 -13 8 36 -13 4 38 -13 0 <== 39 -12 -3 39 -10 -5 38 -7 -6 36 -5 -6 33 -4 -5 29 -3 -3 24 -2 -2 18 -1 -1 11 0 0 5 0 0 0 0 0

Spoiler for That's the same as my first

I had 46, but went in sphere order 2143. My return to origin was much longer than I like.

0,0,0 | 1,-1,1 (going for 2)
1,-1,1 | 2,-2,2
3,-3,3 | 3,-3,3
6,-6,6 | 2,-2, 4
8,-8,10 | 2,-2,5
10,-10,15 | 1,-1,6
11,-11,21 | 0,0,5
11,-11,25 | -1,1,4 (! Going for 1)
10,-10,29 | -2,2,3
8,-8,32 | -3,3,2
5,-5,34 | -4,4,1
1,-1,33 | -5,5,0
-4,4,33 | -5,5,-1
-9,9,32 | -5,4,-2
-14,13,30 | -4,3,-3
-18,16,27 | -3,2,-4
-21,18,23 | -2,1,-5
-23,19,18 | -1,2,-6 (! going for 4)
-24,21,12 | 0,3,-7
-24,24,5 | 1,2,-6
-23,26,-1 | 2,2,-5
-21,28,-6 | 3,2,-4
-18,30,-10 | 4,1,-4
-14,30,-14 | 5,0,-3
-9,29,-17 | 4,-1,-2 (! going for 3)
-5,28,-19 | 5,-2,-1
0,26,-20 | 6,-3,0
6,23,-20 | 7,-4,1
13,19,-19 | 7,-5,2
20,14,-17 | 6,-6,3
26,8,-14 | 5,-7,4
31,1,-10 | 4,-7,5
35,-6,-5 | 3,-6,4
38,-12,-1 | 2,-5,3 (! going for origin)
40,-17,2 | 1,-4,2
41,-21,4 | 0,-3,1
41,-24,5 | -1,-2,0
40,-26,5 | -2,-1,-1
38,-27,4 | -3,0,-2
35,-27,2 | -4,1,-1
31,-26,1 | -5,2,-1
26,-24,0 | -6,3,0
20,-21,0 | -5,4,0
15,-17,0 | -5,5,0
10,-12,0 | -5,6,0
5,-6,0 | -5,6,0
0,0,0 (! origin)

[Smith]

I'd like some clarification, please. In the OP, it states "Before each move, you specify an acceleration vector (a,b,c), where a, b, and c can independently take on integer values from the set (-1, 0, 1)." But it seems to me that both Captain Ed and Molly Mae chose some vector accelerations way beyond these limits. Did I misunderstand?

[curr3nt]

The vectors they listed were the position (and velocity for Molly) not the acceleration.

[Smith]

"I see", said the moderately stupid Smith. Thanks, curr3nt (do you realize how desperately difficult it is to force my finger up to the "3" when I want to type an "e" in your name?).

[CaptainEd]

Spoiler for Slight improvement to 44 steps

Thanks to Smith's reasonable question, I have included ddx, dx and x, as well as column headings. Hope this helps:
mv# ddx ddy ddz dx dy dz x y z
0 -1 1 1 0 0 0 0 0 0
1 -1 1 1 -1 1 1 -1 1 1
2 -1 1 0 -2 2 1 -3 3 2
3 -1 1 1 -3 3 2 -6 6 4
4 -1 0 1 -4 3 3 -10 9 7
5 -1 1 1 -5 4 4 -15 13 11
6 1 -1 0 -4 3 4 -19 16 15
7 1 -1 0 -3 2 4 -22 18 19
8 1 1 -1 -2 3 3 -24 21 22
9 1 1 -1 -1 4 2 -25 25 24
10 1 -1 -1 0 3 1 -25 28 25
11 1 -1 -1 1 2 0 -24 30 25
12 1 -1 -1 2 1 -1 -22 31 24
13 1 0 0 3 1 -1 -19 32 23
14 1 -1 -1 4 0 -2 -15 32 21
15 -1 -1 0 3 -1 -2 -12 31 19
16 0 0 1 3 -1 -1 -9 30 18
17 1 -1 1 4 -2 0 -5 28 18
18 1 -1 1 5 -3 1 0 25 19
19 -1 -1 1 4 -4 2 4 21 21
20 -1 -1 1 3 -5 3 7 16 24
21 -1 -1 -1 2 -6 2 9 10 26
22 -1 0 -1 1 -6 1 10 4 27
23 -1 0 0 0 -6 1 10 -2 28
24 1 1 -1 1 -5 0 11 -7 28
25 1 1 -1 2 -4 -1 13 -11 27
26 1 1 -1 3 -3 -2 16 -14 25
27 1 1 -1 4 -2 -3 20 -16 22
28 0 1 -1 4 -1 -4 24 -17 18
29 0 1 -1 4 0 -5 28 -17 13
30 1 1 -1 5 1 -6 33 -16 7
31 -1 1 -1 4 2 -7 37 -14 0
32 -1 0 1 3 2 -6 40 -12 -6
33 -1 0 1 2 2 -5 42 -10 -11
34 -1 0 1 1 2 -4 43 -8 -15
35 -1 0 1 0 2 -3 43 -6 -18
36 -1 0 1 -1 2 -2 42 -4 -20
37 -1 -1 1 -2 1 -1 40 -3 -21
38 -1 1 1 -3 2 0 37 -1 -21
39 -1 -1 1 -4 1 1 33 0 -20
40 -1 -1 1 -5 0 2 28 0 -18
41 -1 0 1 -6 0 3 22 0 -15
42 -1 0 1 -7 0 4 15 0 -11
43 -1 0 1 -8 0 5 7 0 -6
44 1 0 1 -7 0 6 0 0 0
Sorry about the formatting--I'm failing the editor intelligence test--I have made this be Courier, and manually formatted it with spaces so that everything will align in accurate columns. Unfortunately, you don't get to see that. Sorry...

Edited by CaptainEd, 16 January 2012 - 11:27 PM.

[CaptainEd]

Spoiler for here are 42 steps

It still does not exploit the possibility of a line segment passing through a target, which I'd think would allow more flexibility and a shorter path.

mv#
ddx
ddy
ddz
dx
dy
dz
x
y
z

0

0

0

0

0

0

1

1

-1

0

1

-1

0

1

-1

0

2

1

-1

0

2

-2

0

3

-3

0

3

1

-1

0

3

-3

0

6

-6

0

4

1

0

0

4

-3

0

10

-9

0

5

1

1

0

5

-2

0

15

-11

0

6

1

1

0

6

-1

0

21

-12

0

7

-1

0

0

5

-1

0

26

-13

0

8

-1

1

0

4

0

0

30

-13

0

9

-1

0

0

3

0

0

33

-13

0

10

0

0

-1

3

0

-1

36

-13

-1

11

-1

0

1

2

0

0

38

-13

-1

12

-1

0

1

1

0

1

39

-13

0

13

-1

-1

1

0

-1

2

39

-14

2

14

-1

-1

1

-1

-2

3

38

-16

5

15

-1

0

1

-2

-2

4

36

-18

9

16

-1

1

1

-3

-1

5

33

-19

14

17

-1

1

-1

-4

0

4

29

-19

18

18

-1

1

-1

-5

1

3

24

-18

21

19

-1

1

0

-6

2

3

18

-16

24

20

-1

1

-1

-7

3

2

11

-13

26

21

-1

0

-1

-8

3

1

3

-10

27

22

1

1

-1

-7

4

0

-4

-6

27

23

1

1

-1

-6

5

-1

-10

-1

26

24

1

1

-1

-5

6

-2

-15

5

24

25

1

1

-1

-4

7

-3

-19

12

21

26

1

-1

0

-3

6

-3

-22

18

18

27

1

-1

-1

-2

5

-4

-24

23

14

28

1

-1

-1

-1

4

-5

-25

27

9

29

1

-1

-1

0

3

-6

-25

30

3

30

1

-1

0

1

2

-6

-24

32

-3

31

1

-1

1

2

1

-5

-22

33

-8

32

1

-1

1

3

0

-4

-19

33

-12

33

1

-1

1

4

-1

-3

-15

32

-15

34

1

-1

1

5

-2

-2

-10

30

-17

35

-1

-1

1

4

-3

-1

-6

27

-18

36

-1

-1

1

3

-4

0

-3

23

-18

37

-1

-1

1

2

-5

1

-1

18

-17

38

-1

1

1

1

-4

2

0

14

-15

39

-1

0

1

0

-4

3

0

10

-12

40

0

0

0

0

-4

3

0

6

-9

41

0

1

1

0

-3

4

0

3

-5

42

0

0

1

0

-3

5

0

0

0