Who lives on the ninth floor

Solution

From (i), it is clear that both Q and U are on even numbered floor and since, U is on 2^nd floor, only 4^th,6^th and 8^th floor are there for Q and Y. Since, Y is not above Q, there are two possibilities: Possibility (a) – Q at 8^th and Y at 6^th floor. Possibility (b) – Q at 6^th and Y at 4^th floor. But statement (ii) says, that one who likes white lives on 4^th floor and Y does not like white, possibility (b) is not possible. Hence, we will go with possibility (a) which is Q at 8^th (likes Violet) and Y at 6^th floor. Statement (ii) also says that person on 3rd floors likes Yellow. From (iii), it is clear that the person who likes pink is on the 5^th floor. From (vii), we can say that the person who likes red is on the 9^th floor and also the person who likes purple lives on the 6^th floor . From (v), T is not on the 1^st floor and also since he does not like Yellow, he is not on the 3^rd floor. From (iv), neither W nor R can be at the 9^th floor, as W likes green and R is not at the topmost floor. Also as W likes green, only two floors .i.e 7^th and 1^st, are left for W. Hence, there are two possibilities for W and R : Possibility (a) – W at 7^th floor and R at 3^rd floor. Possibility (b) - R at 5^th floor and W at 1^st floor. But we can see in the above table that T cannot be at 1^st or 3^rd floor. Now (vi), says that there is one floor between the floor on which T and R live. Hence, R also cannot be at 3^rd floor. Therefore, possibility (a) cannot be correct. Hence, we will go ahead with the possibility (b) which is R at 5^th and W at 1^st floor and also from (vi), it is clear that T will be on the 7^th floor. Only colourBlack is left for T, hence T likes Black. From (vi), it is also clear that V and P will be on 4^th and 3^rd floors respectively. Now only person left for 9^th floor is X. Final arrangement will be as follows: