Problem solving using logic - 3 person card game Three logicians played a game with a set of 21 cards each with a different two-digit prime number. Each drew a card and held it up so that they could not see their own card but could see the cards of each of the others. Ali, Bobby and Charlie in turn were then asked two questions, which were "Is your number the smallest of the three?" and "Is your number the largest of the three?". In the first round all three answered "I don't know" to both questions. The same happened in rounds two and three. In round four Ali answered "I don't know" to the first question. What did Ali answer to the second question and what numbers did Bobby and Charlie have?
 A: I don't see a unique solution to this puzzle. 
Before discussing why, let us first assume the cards were just numbered from $1$ to $21$ as there are $21$ cards and exactly $21$ two-digit primes, and all we care about is whether the numbers on the cards are smaller or larger than the numbers on other cards.
So what could Ali's answer be?
There are lots of scenarios where Ali's answer to the second question would be "I don't know" and the numbers of Bob and Charlie could have almost any values.
There's also lots of scenarios where Ali's answer to the second question would be "No" and the numbers of Bob and Charlie could be $21$ and some other number.
There are no scenarios where Ali's answer to the second question is "Yes", as he would then have been able to answer the first question with a "No".
An example of the first scenario would be if the first three rounds had the cards $(9,10,11)$, $(7,8,12)$, $(6,13,14)$ and the fourth round was $(4,5,15)$.
An example of the second scenario would be if the first three rounds were the same as the first scenario and the fourth round was $(4,5,21)$.
