A related game I played with my 7 year old asks for all numbers included in a set. It is an extension of the game where you have to guess a single number and the child learns interval halving. He grew out of that some time ago. I didn't yet leave the natural numbers. As with most question and answer games we change roles. Changing roles has the advantage that there is no "teachers password" effect. And the child has to check the rule more often. After a few dozen rounds he was able to find "1, 3, 8". "all numbers > 0" "all divisible by 10 between -100 and +100", And he invented "only -100", "all divisible by 5 between -100 and 0". The advantage is that you don't need paper and pencil but can do this verbally.