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# Hyperspace Racing

21 replies to this topic

### #1 Molly Mae

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Posted 11 January 2012 - 10:33 PM

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)
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### #2 CaptainEd

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Posted 11 January 2012 - 10:58 PM

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!
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### #3 Molly Mae

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Posted 11 January 2012 - 11:35 PM

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.
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### #4 CaptainEd

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Posted 12 January 2012 - 12:41 AM

Spoiler for my first crack: 46 moves, way suboptimal

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### #5 Molly Mae

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Posted 13 January 2012 - 09:33 PM

Spoiler for my first crack: 46 moves, way suboptimal

Spoiler for That's the same as my first

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### #6 Smith

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Posted 14 January 2012 - 04:32 AM

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?
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### #7 curr3nt

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Posted 14 January 2012 - 04:55 AM

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

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Posted 14 January 2012 - 07:09 PM

"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?).
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### #9 CaptainEd

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Posted 16 January 2012 - 11:17 PM

Spoiler for Slight improvement to 44 steps

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

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### #10 CaptainEd

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Posted 17 January 2012 - 06:21 AM

Spoiler for here are 42 steps

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