Dummy variables question

Suppose you have six categories -- 1, 2, 3, 4, 5, 6.  The question is how many variables do you need for these categories?  You only need 5.  Suppose the variables are is_1, is_2, is_3, is_4, is_5.  You can still identify whether someone's in category 6 because that can be picked out by is_1, is_2, is_3, is_4 and is_5 all being 0.  So the answer's 5.