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