# A puzzle related to three cars which leave a town and reach another.

I'm trying to solve the following puzzle:

$C_1, C_2$ and $C_3$ are three cars that leave town $T_1$ and reach town $T_2$.
For a car, say $C_k, k$ is considered to be the car number. The car number and the order in which they depart or arrive is not the same. The first car to leave $T_1$ is the third car to reach $T_2$.

And the questions are:
$1.$ Which car is the first to leave from $T_1$?
$2.$ Which car is the second to reach $T_2$?

I simply can't think of a way to solve this , The only important given is that "The first car to leave $T_1$ is the third car to reach $T_2$" but how can I possible find the order in which the cars left the town from this ?

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"The car number and the order $\dots$ is not the same." – André Nicolas Sep 30 '13 at 7:35
Hint: neither $C_1$ nor $C_3$ can leave as first car ... – Michael Hoppe Sep 30 '13 at 7:37
@AndréNicolas lol , I mistakenly read it as "The car number and the order … is not neccesarily the same – A Googler Sep 30 '13 at 7:40

## 1 Answer

The key conditions to take into account is the fact that

The car number and the order in which they depart or arrive is not the same.

Spoiler:

The first car to leave $T_1$ cannot be $C_1$ due to the restriction in the problem. Likewise, the third car to reach $T_2$ cannot be $C_3$. This leaves only $C_2$. Thus we know that $C_2$ is the first to leave and the last to arrive. Now, the third car to leave cannot be $C_3$ and thus it must be $C_1$. The first car to arrive cannot be $C_1$ and thus must be $C_3$. This completely determines the orders of the cars. In order of leaving $T_1$: $C_2$, $C_3$, $C_1$. In order of arriving at $T_2$: $C_3$, $C_1$, $C_2$

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