There are two sets of symbols: the four "basic elements" and more complex elements. As you'll recall, the four "basic elements" are earth, water, air and fire (the fifth element is love, in case you couldn't figure that out from the movie). Each of the four basic elements is represented by one of four triangle. They are:
Down-Strike = Earth (amber)
Down = Water (green)
Up-Strike = Air (blue)
Up = Fire (red)
I counted eighteen complex elements. I'm not going to try to describe their symbols (I'll let you handle that), but I will list their names and atomic weights.
Atomic Weight / Name as it appears in the game
05 Boron
12 Magnesium
14 Silicon
15 Phosphorus
16 Sulphur
19 Potassium
26 Iron Mars
29 Copper Venus
30 Zinc
33 Arsenic
47 Silver Moon
50 Tin Jupiter
51 Antimony
78 Platinum
79 Gold Sun
80 Mercury Mercury
82 Lead Saturn
83 Bismuth
So here's my hypothesis:
The complex element symbols on the four cards tell you which numbers to use and the basic elements tell you how to manipulate them (i.e. add, subtract, multiply, divide). My hypothesis states that if you manipulate the numbers correctly, the result will be the number listed in the gray box on the right-hand side.
What still puzzles me is why the planet names are included, but this might just be a red herring.
Escape to Obion Episode 3 - The Alchemist's Notebook
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