On the second day of my holiday, I was at a restaurant with some friends and we had great Mexican food. I paid the bill, which amounted to one-tenth of the money that I carried in. When I left, I noticed that I had as many cents as I had dollars when I went in, and had as many dollars as I had cents when I went in.
With the above information, how many possible values are there for the cost of the dinner?
Note: I had at least 1 and at most 100 coins to start with.