In distinct odd-town, the inhabitants want to number their houses with 3-digit positive integers that are odd, which have all distinct digits. What is the maximum number of houses in odd-town?
Details and assumptions
The number \(12 = 012\) is a 2-digit number, not a 3-digit number.
Clarification: No 2 houses may have the same house number.
\(123\) is a valid house number, as it is a 3-digit number, odd, and has distinct digits.