Question
Which of the following Flat is
vacant? Answer the questions based on the information given below. Eleven persons A, B, C, D, E, F, G, H, I, J and K live in four storey building having four floors such that lowermost floor is numbered as 1 and floor immediately above the lowermost floor is numbered as 2 and so on. Each floor has 3 flats numbered as 1, 2 and 3 from west to east such that flat β 1 is in west of flat β 2 and flat β 2 is in west of flat β 3. One of the flats on a floor is vacant. The dimensions of each of the flats are same. Note: If there is one/two floor(s) between two flats then they may or may not have the same flat number of different floors. K lives in an even numbered flat on floor number 2. B and C live on same floor. B lives in an even numbered flat on lowermost floor. G and A live on same floor. All the flats on the floor on which F lives are occupied. I lives to the west of G. B lives on the floor on which two other persons live. There is one floor between G and F. Eβs flat is immediately above Cβs flat and the numbers of their flats is same. G lives immediately below the vacant flat and the flat number of vacant flat and G is same. D lives somewhere above J in same flat number, but not on flat 3.A lives in flat β 1.Solution
1. B lives in an even numbered flat on lowermost floor i.e. B lives on floor ground floor in flat 2. 2. K lives in an even numbered flat on floor number 2. B and C live on same floor. E lives immediately above Nand the numbers of their flats is same. So, Now, C either lives immediate west or east of B which means E either lives in flat 3 or flat 1. So, we have two possibilities. Case I: When C and E live on flat β 3: 
3. G and A live on same floor. I lives to the immediate west of G. G lives immediately below the vacant flat and the flat number of vacant flat and G is same. A lives in flat β 1. There is one floor between G and F. Now, G lives immediately below vacant flat so, the vacant flat must be in topmost floor. Case I: When C and E live on flat β 3: 
5. D lives somewhere above J in same flat number, but not on flat 3. Now, we cannot fix D and J in same flat number in case II, so, case II is invalid. The final arrangement is as follows 
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