Probably helped reduce clerical errors as Dennis posted, but not terribly
effective. The Kansas City Southern's use of "check digits" worked far better
(the last digit being a computed function of the preceding digits).
In at least one case the C&NW "backfilled" a series with ODD numbered cars,
so it's also possible that even & odd digit numbering helped when the number
of cars needed might increase over time, without having to carve out another
Probably to make it look they had more cars than they actually had.