Transformation Puzzle

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Nov 8, 2014
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So I have the table below it is part of a puzzle I am trying to work through and I'm looking for help with both the mathematical vocabulary to describe it and ways to solve it.

The first stage of the task is to pick three elements from the left of the table and use the numbered functions along the top to "change" the elements twelve times and on the final (twelfth) change to have all elements transformed into “Ag” (silver). The functions can be used in any order so long as there are no repeats.

So if you say start with the elements Cu, Pb and Fe (Copper, Lead and Iron) and pick function 6 as you first move, you follow the table along to see what it then becomes under that function, so:

Cu becomes Zn
Pb becomes P
Fe becomes S

Then you pick function 18 as your next move:

Zn becomes Bi
P becomes Ag
S becomes Ar


And so on until all three elements have become Ag within 12 moves.

Alchemy Table.jpg



The second stage is to do the same but with two sets of three elements, there can be overlap in the elements chosen but no overlap in the functions used and the third stage is the same again but with three sets of three elements.

So I can do this by eye, trying it out one at a time following through patterns looking how to condense elements into a single one before changing it into Ag. But there must be an easier way to test this.

Any help would really be appreciated.

Thank you
 
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