This is just out of curiosity.
Let's say there is a group of people, $A$, that never met each other before. The size of $A$ is $|A|=N$. In $A$, there are people, $a_i$, where $1 \leq i \leq N$. Now, we will let people in $A$ start wandering around randomly in a huge vacuous room with total random moves. What is the minimum positive integer $N$ that every person $a_i \in A$ would feel seeing a new person everytime he/she sees a person?
In general, let's say you are living in a city. How small the population of the city, $N$, could be so you would feel like you don't see a person that you remember seeing before under an assumption of random movements?
Is there a mathematical finding that reveals such number $N$?
Modified: After talking with Alex, it was clear that the answer to this question would be more suitable for the psychology stack exchange. So I would like to modify the question a little bit:
Let's say we know the number $n$ that promises a person would remember seeing another one. For example, after $a_i$ sees $a_j$ and sees $n-1$ different $a_k, a_k \in A$, and sees $a_j$ again, we know that $a_i$ remembers seeing $a_j$. Also, instead of the unclear randomness of seeing while walking, let's say they are in a handshaking environment where they must handshake with one and with another after. The person would choose next person to shake hand randomly but it can't be the one whom he/she just had a handshake with. In such a setting, what is the minimum $N$ that we could promise all $a_k, a_k \in A$ that they will never handshake with any person they remember?