A/The Number Of...
The number of post offices here have actually increased (Straits Times, 25 March 2009) is wrong.
Make it has, since the verb agrees with the head noun number. When we use the number of, we are really referring to a number.
By contrast, a number of functions as a quantifier, akin to some or a few, so the verb agrees with the head noun:
A number of post offices have shut down this year.
The same rule applies to total: A total of 54 applications have been received, but The total of 54 applications is far higher than we had expected.