In a recent match, the team didn't do so well: the total number of waves that the cheerleaders gave was fewer than 50.

If I told you what that total number of waves was, you'd be able to deduce that the number of occasions on which they waved could be any of three different possibilities. Even if I then told you on how many occasions they waved, you could still find three different orders of 6's and 1's scored that would have led to that total number of waves.

On how many occasions did they wave, and what was the total number of waves?