Hello,

Yes

Why ?

I don't know and I don't even know the exact definition of an orthogonal array

The thing :

«If we know that a coin is lighter (it may go the same way if it's heavier) than the N other coins, and if $\displaystyle 3^{n-1} \leq N < 3n$, the dud can be found in a maximum of $\displaystyle n$ weighs.»

The thing to do is to divide the set of coins into 3 subsets, 2 will have the same number of coins, which we are going to put in the balance, and the third one (which has less or as many coins as the other sets) aside.

A weigh lets us know in which of the subsets there is the dud.

And so on..