Look for help with this problem. I realise it's not the most clear the way it's written but it's difficult to phrase.
Imagine you are assigned x items. You are then given y sets of size z each, which contain between them all between 0 and x of your items, and the remainder of each set is filled with items you were not assigned. There are no two items the same between sets.
You draw a number of items from the sets at random. You can't tell what you're drawing from the set until you've made your final selections. You're trying to pick all your items with no incorrect selections. So the number you select will be between 0 and x.
For example, say you were assigned 5 items and there are 3 sets of size 9 each. When generating the sets, you first pick randomly how many items out the 5 you will spread across the 3 sets and fill the rest with decoy items until you reach 9. So for example say you chose to select 4. You first have to pick 4 out the 5 (5choose4), then assign them to sets. Assigning them could be done like 4, 0, 0 .... 4, 0, 0 .... 0, 0, 4 ... 0, 0, 4 .... 3, 1, 0 .... 3, 0, 1....etc...
The aim of the game is to correctly select all 4 items from the sets. You make selections from set 1, then set 2 and finally 3. You don't know how many items you're looking for, it could be 0 to 5. The selection is only a match if it matches exactly, i.e. you can't miss any you were assigned residing in the sets and you can't select items from the set that you weren't assigned originally. How many rounds would have you to play before you had covered every possibility?