195877

Our solution is for the 0-9 dominoes. We lay the dominoes out in rows in order of the number on the top of the domino. When we finished laying them out, the pattern looked like a staircase because each one of the dominoes in the row below had been already used in the one above that.
We counted the pattern - it went 1+2+3+4 and so on until +10. This equals 55 dominoes. We checked we were correct by counting the dominoes one by one. Our domino set was like the one described in the problem, the box was broken and not all the dominoes were there so we had to use dominoes from another set and we even had to draw one.