Distinct Odd-Town

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.


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