Four of the following five are alike in a certain way

Solution

B lives in an odd numbered floor. There is a gap of two floors in which B and A lives. Both A and B do not live in the same flat number. E lives immediately above A in the same flat number. From these statements we will have four cases: If B lives on fifth floor in flat 1, then A lives on second floor in flat 2. As E lives immediately above A in the same flat number. So, E will live on third floor in flat 2. If B lives on first floor in flat 1, then A lives on fourth floor in flat 2. As E lives immediately above A in the same flat number. So, E will live on fifth floor in flat 2. If B lives on fifth floor in flat 2, then A lives on second floor in flat 1. As E lives immediately above A in the same flat number. So, E will live on third floor in flat 1. If B lives on first floor in flat 2, then A lives on fourth floor in flat 1. As E lives immediately above A in the same flat number. So, E will live on fifth floor in flat 1. Both E and G lives in the same flat number.C and F live in the same floor. (vi) J, who lives on an even numbered floor, lives below F and both lives in the same flat number. From these statements Case 2 and Case 4 will get discarded as G lives on third floor. C and F live on same floor and J lives below F in even number floor which can’t be possible. So, we will proceed with Case 1 and Case 3. Case 1. F cannot live on fourth floor in flat 2 as J lives below F in even number floor. So, F and C will live on fourth floor in flat 1 and flat 2 respectively. Then J lives on second floor in flat 1. Case 3. F cannot live on fourth floor in flat 1 as J lives below F in even number floor. So, F and C will live on fourth floor in flat 2 and flat 1 respectively. Then J lives on second floor in flat 2. H does not live in flat number 2.There is a gap of one floor in which E and G lives. I lives above D and both live in the same flat number. H and D neither live in the same flat number nor in the same floor. Case 1. I and D cannot live in flat 2 as there is a gap of one floor in which E and G lives. So, I and D will live on third floor and first floor in flat 1. H and D neither live in the same flat number nor in the same floor. H cannot live on first floor with D. So, H live son fifth floor in flat 2 but this case will get discarded as it is given that H does not live in flat number 2. Case 3. I and D cannot live in flat 1 as there is a gap of one floor in which E and G lives. So, I and D will live on third floor and first floor in flat 2. H and D neither live in the same flat number nor in the same floor. H cannot live on first floor with D. So, H live son fifth floor in flat 1 and G lives on first floor in flat 1. Final arrangement as shown below: