The Archaeologist (Posted on 2008-12-05)

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.

	Submitted by brianjn
No Rating
Solution:	(Hide)
The assistant offered the archaeologist four options, two had cyan in the second top layer while two had orange as that layer. In both latter options downward descents are from F in the magenta and cyan tiers. With the order being magenta, cyan, orange, yellow, the drawn paths have 40 and 42 rightangles. The archaeologist's choice is: Magenta: D H G C B A E I M N O P L K J F [9 line segments, 8 rt. angles], Cyan: F E A B C D H G K L P O N J I M [12 line segments, 11 rt. angles], Orange: M I J N O P L K G H D C B F E A [13 line segments, 12 rt. angles], Yellow: A E F B C D H G K J I M N O P L [11 line segments, and one for "out", 11 rt. angles]. I leave the solver to determine the other options already mentioned.

	Subject	Author	Date
	Puzzle Thoughts	K Sengupta	2024-01-10 11:13:32
	Possible Solution	rod hines	2008-12-05 16:44:02