Here's an example of play leading to discovery of an inorganic formula. It illustrates the kind of strategy, based on chemical knowledge that expert players use.
We'll assume that all of the compounds in the database are inorganic salts. (Organic compounds are generally inappropriate, since their molecular formulas are not very informative, and there are no well-defined rules for the sequence of elements.)
Here's how the formula may appear at first:
?e ?n (?e ?n ?e ?n) ?n
This already contains a lot of information. There would appear to be a metal cation and a complex anion such as OH or SO4. Because the brackets are there, we also know that the last number can't be 1, as in Na2SO4.
It is always a smart move to clear away the near-certainties as soon as possible. Most anionic complexes have only a single central atom, so try 1 for the second number. It's correct.
?e ?n (?e ?e ?n) ?n
If the anion has charge 1-, the first number will be 1. Try it.
?e (?e ?e ?n) ?n
Right again. So we are looking for univalent groups like OH, CN, NO3, etc. We can sort them out by trying 1 for the first of the remaining numbers. This produces the feedback "No. It's bigger than that". So we've eliminated OH, SH, CN, and so forth.
Most likely the anion contains oxygen. So try oxygen in the last element place:
?e (?e O ?n) ?n
Right again. Most of the oxygen-bearing anions with charge -1 have three oxygens (NO3, ClO3, etc.). So try 3 just before the bracket:
?e (?e O3) ?n
For the second element, nitrogen is an obvious choice. We get the feedback "No. It is a nonmetal". So try chlorine.
?e (ClO3) ?n
Rather than guess metals at random, we can use the number after the bracket to sort them out by charge. This number is most likely 2 or 3. It can’t be one, or there would be no brackets, but it could be larger then 3. A guess of 3, if wrong, produces the most useful feedback, which turns out to be "No. It's smaller than that". So it must be 2:
?e (ClO3)2
Go where there are lots of 2+ metals and try calcium. The feedback is "No. It's a metal". This eliminates all of the transition elements. Since we were not told we were in the correct group, it also eliminates the Be-Ba group. Of the remaining reasonable possibilities, there are three metals in the Zn-Hg group and two in the Sn-Pb set, so play the odds and try Zn. This time the feedback tells us we're in the right group.
Cadmium produces the feedback "No. Its oxide decomposes when heated". This suggests mercury, which of course is the only remaining element in the group.
Hg(ClO3)2
Since we used six wrong guesses to elicit the necessary information to solve this formula, our score is 20 - 6 = 14.
This example illustrates the kind of chemical logic that can be used in the Formula Game as one becomes more expert. Incidentally, this example was a rather tough one.
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Updated July 18, 2000