Answer:

Yes, easily.

How to tell Hats from Ties

hat and tie

You feel like stepping out for the night, and look at your collection. You decide to wear

 
hat 73 
tie 19

No problem.

There are two things that are needed to ask for an item:

  1. The name of the collection ("hat" or "tie").
  2. The item number.

The numbering scheme within one collection is independent of other collections. You can have hat number 13 and also have tie number 13, assuming that both exist.

QUESTION 3:

Say (as before) that you have 500 hats. Can you ask for hat number 577?