Pandigital Products
We shall say that an $n$-digit number is pandigital if it makes use of all the digits $1$ to $n$ exactly once; for example, the $5$-digit number, $15234$, is $1$ through $5$ pandigital.
The product $7254$ is unusual, as the identity, $39 \times 186 = 7254$, containing multiplicand, multiplier, and product is $1$ through $9$ pandigital.
Find the sum of all products whose multiplicand/multiplier/product identity can be written as a $1$ through $9$ pandigital.
HINT: Some products can be obtained in more than one way so be sure to only include it once in your sum.