From the scant knowledge of this culture, a time-worn artwork and a partly restored "map" found within the ruins of his current study, the archaeologist concluded that:

1. the structure of his study had been a 4-tiered 4 x 4 array of rooms.

   (He designated the layout of each tier as:
                A B C D
                E F G H
                I J K L
                M N O P   )

2. in the passage from top to bottom all rooms would be visited just once before moving to a lower level,
   
   and
   
3. the last element in his map (yellow) was clearly the ground floor of this ancient remnant.

"Sir," uttered his assistant displaying a set of diagrams, "I believe these are all possible routes through this structure. While you did insist that a speed challenge may be involved, and two have the least turns, one may be of greater interest."

Eyebrows quizzically raised the archaeologist queried, "And that would be ...?"

"This! 'Four' may have been highly significant to them. This structure is four tiers of 4 by 4 rooms. In this scenario each path has the same number of turns per tier ... and ... that total is divisible by 4!"

Determine, at least, the layout which the assistant most prized.

Initial assumptions:  Yellow is given as the ground floor, on which the 4x4 grid of rooms A to P is super-imposed.  Presumably the lines indicated are walls that still remain standing which then block moves, force turns, etc.  (The outer openings in the yellow and magenta tiers suggest doors, which the other two tiers don't have, so they too must just be missing walls.)  All investigations begin and end in outer rooms of the grid.

Big assumption:  While all tiers have the same number of turns, it's implied that this number is divisible by 4 (e.g. 12), which I couldn't get to work for every tier.  I'm going with the obvious...that the total refers to that of all four tiers (having the same number of turns each) which will of course always be divisible by 4!

So, if I have this correctly, all tiers/rooms can certainly be explored with paths having 10 turns each as follows (* indicates a turn, and the paths work in reverse):

Yellow:  (Start) A-E*F*B*C-D*H*G*K*J-I*M*N-O-P*L (end)

Blue:  (Start) I-M*N*J-F*E*A*B-C-D*H*G*K-O*P*L (end)

Magenta:  (Start) I-M*N-O-P*L*K-J*F*E*A*B-C*G*H*D (end)

Orange:  (Start) M-I*J*N*O-P*L*K*G*F-E*A*B-C-D*H (end)

 

Edited on December 5, 2008, 4:47 pm

Edited on December 5, 2008, 4:54 pm

Posted by rod hines on 2008-12-05 16:44:02