Is this a well-known game? In the last two days, I got a bit obsessed with the following game, partly because I beat others most of the time I play it. The gamers are expected to have a sound logical reasoning coupled with the ability to analyze data.
Here is the rule of the game:
$(1)$ The game is for two players.
$(2)$ Each player holds a $4$-digit positive number in his mind. (Numerals $0$ to $9$ are allowed. For instance you can hold $0176$ or $5678$ or $2384$, etc.)  The numbers are to be kept secret.
$(3)$ Each then guesses the other's $4$-digit number. 
$(4)$ Each person gives a mark for the other person's guess. The mark consists of two parts. The first part counts the number of digits the other person rightly guessed. The second  part counts the number of digits that were guessed in the right place. 
$(5)$ The fist person who comes to the right $4$-digit the other person held is the winner.
Here is a sample where the players are Mr.A and Mr.B. Assume A has held $3476$ and that B has $7609$. Let A begin. 
\begin{vmatrix}
 \hline
   \text{Player(A)}   & \text{Correct digits} & \text{Correct places} & \text{Player(B)}  & \text{Correct digits} & \text{Correct places} \\ \text{guesses} & \text{(B-  marks)} & \text{(B-marks)}
&  \text{guesses} & \text{( A- marks)} & \text{( A-  marks)}\\
   4521             & 0                       & 0                       & 5735             & 2                        & 0                        \\ 
   8309             & 2                       & 2                       & 8762             & 2                        & 0                        \\ 
   ...              & ...                     & ...                     & ...              & ...                      & ...                      \\ 
   7609             & 4                       & 4                       & 3467             & 4                        & 2                        \\
  \hline
\end{vmatrix}
So A is the winner. There is a lot of mathematical elimination strategy going in there  which makes the play a very interesting pastime at least for me. If this is a known game, could you please point me to a reference? Thank you.

Seems like a variant of Mastermind. I believe it is called Cows and Bulls.
