By 'real' I mean one of the first solutions proposed.
By mathematically induced I mean a solution comprised of (or proved from) mathematical formulae and properties.

That's OK. Clearly, no offense was intended, nor any was taken.
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>By 'real' I mean one of the first solutions proposed.

No one solution os more 'real' than the next. I think solutions to a problem may be categorized as more or less useful, or, say, more or less elegant. One solution is more useful than another if it's less ad hoc, i.e. if it applies to a wider range of problems. Whether a solution is elegant is often in the eyes of a beholder. I personally think that Jack Wert's solution is the most elegant and also find it the most useful, because of the immediacy with which it extends to a larger number of coins.

>By mathematically induced I mean a solution comprised of (or
>proved from) mathematical formulae and properties.

Mathematics is more about formal reasoning than about using formulas. Math language is just a tool that helps make a problem more manageable.

Jack Wert's solution does not use any formulas, but only common sense. However, the reasoning is quite formal. So I would not deny it the mathematical nomenclature.