Anyway, there are 17 sickles to the galleon and 29 knuts to the sickle. Naturally--well, enough for a recreational mathematician--I wondered if there were amounts of money which, when doubled, transposed the numbers of each coin type. Short answer, yes.
First, a ground rule. Just like you wouldn't say something costs one dollar, two hundred ninety-nine cents, neither should the amounts of wizarding money be named with more than 16 sickles or 28 knuts. Alternatively phrased, an amount of money should always use a galleon when there's an option to use 17 sickles or 493 knuts, and a sickle when there could be 29 knuts.
So now I won't keep you waiting. There are three unit prices (I think), besides free, where the price of one and the price of two use the same numbers of coins in a different order. Find them.