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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 1

up vote 3 down vote accepted

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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