Q-bert Quizzler
Ted S.
gameboard of blocks to make the block faces show the desired color, all the
while avoiding a series of bouncing balls and various other fatal-to-Qbert
objects. The board looked more or less like this (as best as one can do in
ASCII to show the object of the game!):
*
/ \
* *
/ \ / \
* * *
/ \ / \ / \
* * * *
/ \ / \ / \ / \
* * * * *
/ \ / \ / \ / \ / \
* * * * * *
/ \ / \ / \ / \ / \ / \
* * * * * * *
(ie. seven rows of one to seven blocks, for a total of 28 blocks, set in a
triangle)
Where each * represents one of the block faces on which Qbert can jump, and
the diagonal lines represent the paths Qbert can legally use to get from
one block to the next. In each round, Qbert starts from the top block.
There were five different levels in the game, with the following color
change sequences (different actual colors were used, but for the point of
this puzzle, the starting color will be designated Color #1):
Level 1: 1 (starting color) -> 2 -> 2 (end color; jumping on a block of
this color does nothing)
Level 2: 1 -> 2 -> 3 -> 3 (Color #3 is end color; jumping on a block of
this color does nothing)
Level 3: 1 -> 2 -> 1 -> 2 ... (Color #2 is required color, *BUT* jumping on
a block of this color always changes it back to the starting color)
Level 4: 1 -> 2 -> 3 -> 2 -> 3 ... (Color #3 is the required color, *BUT*
jumping on a block of this color always changes it back to the intermediate
color)
Level 5: 1 -> 2 -> 3 -> 1 -> 2 -> 3 ... (Color #3 is the required color,
*BUT* jumping on a block of this color always changes it back to the
original color)
In each of the five levels, what is the quickest legal path (ie. the
smallest number of moves, where any jump from one block to the next counts
as one move) for Qbert to complete the board? Assume, of course, that
Qbert has complete freedom to move wherever he wants around the board
without having to worry about foreign objects (unlike the real game), but
that all Qbert's moves are legal.
--
Ted Schuerzinger
fe...@bestweb.net
Peter Morris
"Ted S." <fe...@bestweb.spam> wrote in message
news:g0o2b41vrjs1.n...@40tude.net...
In addition there were two "elevators" that you could use to lift you up
to the top cube.
> --
> Ted Schuerzinger
> fe...@bestweb.net
Mike Keith
>to the top cube.
>
I'm not sure it was always two, and I'm positive that they weren't in the same
place on each level. It would make an interesting variation on the OP's puzzle
to include the elevators, but that would require knowing where they were.
Ted S.
I think they were called transporters, but in the version of the game I
have on my PC, the number and location of them definitely changes. Of
course, I don't know exactly how true to the arcade game this PC version
is.
I deliberately didn't mention them because they change location, and
because I thought the question was complicated enough as it is. I presume
the usual suspects are writing C programs to solve this question even as I
type. :-)
--
Ted Schuerzinger
fe...@bestweb.net
The Qurqirish Dragon
>
>>>In addition there were two "elevators" that you could use to lift you up
>>>to the top cube.
>>>
>>
>> I'm not sure it was always two, and I'm positive that they weren't in the
>same
>> place on each level. It would make an interesting variation on the OP's
>puzzle
>> to include the elevators, but that would require knowing where they were.
>
>I think they were called transporters, but in the version of the game I
>have on my PC, the number and location of them definitely changes. Of
>course, I don't know exactly how true to the arcade game this PC version
>is.
They were called "disks" and they did indeed change location and quantity. In
the original arcade game, there were 2 disks in level 1, 3 in level 2, 4 in
level 3 (except round 4 which only had 3), 5 in level 4 (except round 4, which
had 3), and for levels 5 and up, there were 6 disks in round 1, 5 in round 2, 4
in round 3, and 3 inround 4.
Anyway, the interesting thing was that in the levels where you had the
1->2->3->1 pattern, it was possible to have the parity of the blocks wron- and
so you could not clear the level without using a disk (on an odd-numbered row,
this would change the parity), or waiting for one of those guys that turned the
colors back on you.
But back to the OP:
I will only do level 1 (1->2->2):
there are 28 spaces to get to (including returning to the top at some point,
since a color is changed by arriving there, not starting there), so 28 is a
theoretical minimum. This cannot be attained, however.
Every jump goes between an odd row and an even row. there are 16 (1+3+5+7)
cubes in odd rows, and 12 (2+4+6) on even rows. Since you start in an odd row,
you need to make a minimum of 32 moves.
calling the rows 1..7, and the cubes a..g, here is a 32-move solution:
start(1a)-
2a-3a-4a-5a-6a-7a-6a-7b-
6b-5b-4b-3b-2b-1a-2b-3c-
4c-5c-6c-7c-6c-7d-6d-5d-
4d-5e-6e-7e-6e-7f-6f-7g.
Finding a (minimum) 64-move solution for the 1->2->3->3 is a fairly simple
exercise, given the level 1 solution.
The levels where colors revert after the goal color should be more
interesting...
--
The Qurqirish Dragon, posting from his home somewhere in Ohlam.
--==<<{{ UDIC }}>>=--
Remember- my address is no laughing matter
Ted S.
> Anyway, the interesting thing was that in the levels where you had the
> 1->2->3->1 pattern, it was possible to have the parity of the blocks wron- and
> so you could not clear the level without using a disk (on an odd-numbered row,
> this would change the parity), or waiting for one of those guys that turned the
> colors back on you.
Are you suggesting that from the start, it's impossible to complete the
boards on Level 5 without using one of the disks or waiting for the color
change guy (or, alternatively, sacrificing a life by jumping off the board,
at which point you get sent back to the top)? I'd like to see a proof of
this.
Of course, if you can complete a board on Level 5 before the color change
guy comes, more power to you. :-) I finally broke 100K on the version I
have, losing (IIRC) on Round 2 of Level 5. I was racking up a ton of
points simply by going around in circles, it seemed.
--
Ted Schuerzinger
fe...@bestweb.net
The Qurqirish Dragon
No, I was not suggesting that you might start in an impossible situation- just
that it often occurred. While playing the game, I am more worried about
avoiding the obstacles than the parity of the pyramid :-)
A quick sketch showed me that it is indeed possible to do the 1->2->3->1
pattern without a disk/sam/slick. This pattern is 71 jumps. The theoretical
minimum (by my previous parity arguement) is 64, since there are 32 odd-level
changes needed and every other jump is onto an odd level.
* denotes platform has reverted to color 1
start:
2a - 1a - 2a - 1a - 2b - 3b -2b - 3b -
4b - 3a - 4b - 3a - 4a - 5a - 4a - 5a -
6a - 7a - 6a - 7a - 6a*- 7b - 6a - 7b -
6a - 7b*- 6b - 7b - 6b - 7b - 6b*- 5b -
6b - 5b - 6b - 7c - 6c - 7c - 6c - 5c -
4c - 5c - 4c - 3c - 4d - 3c - 4d - 5d -
6d - 5d - 6d - 7d - 6d*- 7d - 6d - 7e -
6d - 7e - 6e - 5e - 6e - 5e - 6f - 7f -
6f - 7f - 6f*- 7g - 6f - 7g - 6f
After writing this, I found (by hand) a 65 step solution. This path is the
minimum, since any solution must have 56+3n jumps (28 spaces*2 changes, plus
any reverted cube needs 3 more to get to the end. The first value of 56+3n that
is over the 64 minimum I gave before is n=3, or 65.)
Finding this path is left as an exercise to the reader. 20 lines after the end
of this post, I will give the three cubes that I reverted as a hint.
I used to be a master of this game in the arcade. The last time I played it in
the arcade, I played for over an hour on one credit, and then got tired and
committed suicide in the game 11 times in a row (you couldn't have more than 11
lives at a time)
As for going in circles, once you are at a level where colors revert, this was
possible. In the arcade and colecovision versions of the game, you got 15
points any time you changed a cube's color (25 if it became the destination
color), so if you never cleared such a leve, you could build a huge score.
However, since level-clear bonuses are over 3000 by this time, you could score
a lot faster by finishing the level. Of course, if you couldn't handle a higher
level this was still an option.
**hint 20 lines down**
15
10
5
In my minimum solution, cubes 6a, 6d, and 6f are reverted once each. The path
ends on 6f.