Z-matrix
The first time I met team@ was after a nocturnal mtb ride. I came home just after GC2GP9G had been released, and as it was a quick solve there was nothing else to do but head back out in the snow for another ride. Anders and Tiina met up at GZ with some refreshments and we had a nice chat.
There have been a lot more chatting since then. We have discussed puzzles, been on caching trips and FTF hunts, organized events, his alter ego Turaga Vakama has given invaluable feedback on my plans for new caches... and of course there has also been a lot not related to geocaching.
As we first met at a chemistry puzzle, it is only fitting that this puzzle also is about chemistry. It has been great knowing you, I hope you would have liked solving this puzzle!
Description
A z-matrix is a representation of a molecule using internal coordinates. Each line represents one atom, giving its atomic number and its distance, bond angle and dihedral angle to given atoms in the system. For example, the line
C 1 1.00000 2 60.00000 3 180.00000
is interpreted as a carbon atom 1 Å away from the atom on line#1, the bond angle x-1-2 is 60° and the dihedral angle x-1-2-3 is 180°.
The first three lines only give a limited set of information as you will need two points to specify a distance, three points to specify an angle and so on.
There is no information given as to which atoms are bound together, as that simply is a function of their relative positions.
The following is a somewhat scrambled Z-matrix of a structure of cinnamic aldehyde:
C C 1 2.48876 C 1 2.42055 2 122.61753 C 3 2.42344 1 60.11804 2 359.97438 C 2 2.44845 1 174.40135 3 180.02562 C 1 1.40694 2 31.89436 3 359.97438 C 3 1.39526 1 29.96234 2 179.97438 C 2 1.34557 1 154.35427 3 359.97438 C 3 1.39565 1 90.01946 2 359.97438 O 5 1.22009 2 148.24190 1 179.97438 H 5 1.08589 2 92.31385 1 359.97438 H 8 1.08152 2 121.68230 1 0.02562 H 2 1.08783 1 87.53102 3 179.97438 H 1 1.08332 2 88.44090 3 179.97438 H 7 1.08239 3 119.92188 1 180.02562 H 3 1.08237 1 149.97050 2 179.97438 H 9 1.08248 3 119.83217 1 180.02562 H 4 1.07823 3 147.74639 1 180.02562
Your task is to calculate the sums of the bond lengths for the ring and the chain, respectively. To transform these into a coordinate for the checker, use the integers as degrees and the decimals as minutes, i.e. a sum of 12.34567Å for the ring becomes N12° 34.567.