Who Stays Where?

Let $A,B,C,D,E,F$ represent the floor each of the tenants (as listed) resides on. From the first and fourth conditions we know that $A$ and $C$ can only be one of $1,3$ or $5$ . Then from condition 5 we see that $B$ must also be odd, (as it must differ from $C$ by 2). So $(A,B,C)$ must be some ordering of the three odd-numbered floors, but as $B$ and $C$ must differ by 2 we see $A$ cannot be $3$ , as this would result in $B$ and $C$ differing by 4. Thus the possible orderings for $(A,B,C)$ are $(1,3,5), (1,5,3), (5,1,3)$ and $(5,3,1)$ .

The third condition implies that $C = E + 1$ , which in turn implies that $C \gt 1$ , thus eliminating $(A,B,C) = (5,3,1)$ . This also means that $E$ must be one of $2$ or $4$ .

The second condition implies that $|A - F| = 3$ , so since $A$ can be one of $1$ or $5$ we see that $F$ must be one of $2$ or $4$ . Also, since none of $A,B,C,E$ or $F$ can be $6$ we have by default that $D = 6$ , (with none of the given conditions contradicting this conclusion).

We then have that $(E,F)$ is one of either $(2,4)$ or $(4,2)$ . So, with $C = E + 1$ we have that $(A,B,C,D,E,F)$ is one of $(1,3,5,6,4,2), (1,5,3,6,2,4)$ or $(5,1,3,6,2,4)$ . But then as we require that $|A - F| = 3$ we are left with one possible option satisfying all the given conditions, namely $(A,B,C,D,E,F) = (1,5,3,6,2,4)$ .

Finally, with $B = 5, C = 3$ and $F = 4$ the person living on the floor between those occupied by Binay and Chandan is $\boxed{Farhad}$ .

Arun lives on an odd numbered floor, then the three possible floors are 1,3 and 5. But there are 2 floors between Arun and Farhad, then Arun cant be on 5th floor, because then Farhad should have to live on the 7th floor which does not exist.

Lets look what happens if Arun lives on the third floor. The fourth statement states that Chandan does not live in an even-numbered floor, which implies that he lives on an odd-numbered floor. Now as Arun has already occupied the third floor, Chandan has no choice but to occupy the first floor or fifth floor. But according to the third condition Chandan lives above Etihad, but this condition is not satisfied because there is no floor below floor 1. So, Chandan does not live in floor 1.

Now, what if Chandan lives in floor 5? Then Etihad lives in floor 4.And according to the second statement, Farhad lives 2 floors above Arun i.e 3 + 2 = 5th floor. Then the only persons left are Bonay and Deepesh. Who has two floors vacant:- First and second. If Deepesh is placed on the second floor and Binay on the first, there are three persons between Binay and Chandan, namely, Ethihad, Arun and Deepesh, which violates the fifth statement. If Binay is placed on the second and Deepesh on the first, there are 2 persons between Chandan and Binay, namely, Ethihad and Arun which again violates the fifth statement.

Now, what is Arun is placed on the first floor, then Farhad should be on the fourth floor. Let us place Chandan on floor 5, then Ethihad should live on floor 4 which is already occupied by Farhad, so Chanadan does not live on floor 5.

We cannot place Deepesh on the fifth and Binay on the sixth which violates the fifth statement because 2 people live between Chandan and Binay namely, Farhad and Deepesh.

Then lets place Chandan on floor 3, then Ethihad lives on floor 2. Placing Binay on fifth floor and Deepesh on the sixth gives that only one person lives between Chandan and Binay, ie. Farhad, it satisfies all the conditions of the question.

So, the answer is $\boxed{\text{Farhad}}$ .

If A lives on first floor, F stays on fourth floor. C and E live on consecutive floors in this order. So they can stay on floor 2,3 or 5,6. Since C cannot stay on an even floor, C has to stay on floor 3. E stays on floor 2. B stays on floor 5 and D stays on floor 6. The correct order: