Twelve people (From M to X) live in a sixteen storey building, where ground floor is numbered as Floor 1 and the topmost floor is numbered as Floor 16. Five of these people like Red colour, three like Green colour and the rest like Blue colour. Only one person lives on each floor. Persons live in the building in such a way that all the persons who like the same colour are clustered together with no empty floor between them and at least one empty floor between the people who like different colour. At most two empty floors can have consecutive numbers.
So,
The total number of people who like Red colour = 5
The total number of people who like green colour = 3
The total number of people who like blue colour = 12 - 5 - 3 = 12 - 8 = 4
| Floor | Person | Colour |
| Floor 16 | | |
| Floor 15 | | |
| Floor 14 | | |
| Floor 13 | | |
| Floor 12 | | |
| Floor 11 | | |
| Floor 10 | | |
| Floor 9 | | |
| Floor 8 | | |
| Floor 7 | | |
| Floor 6 | | |
| Floor 5 | | |
| Floor 4 | | |
| Floor 3 | | |
| Floor 2 | | |
| Floor 1 | | |
· W lives on 16th floor.
· P, Q, and R like blue colour and live in consecutively number of floor in increasing order respectively after all the persons who like Red and green
· So, we can conclude from these two statements that P, Q, R and W like Blue colour and like on floor 13, 14, 15 and 16 respectively.
· Moreover, Floor 12 will be a vacant floor.
| Floor | Person | Colour |
| Floor 16 | W | Blue |
| Floor 15 | R | Blue |
| Floor 14 | Q | Blue |
| Floor 13 | P | Blue |
| Floor 12 | Vacant | |
| Floor 11 | | |
| Floor 10 | | |
| Floor 9 | | |
| Floor 8 | | |
| Floor 7 | | |
| Floor 6 | | |
| Floor 5 | | |
| Floor 4 | | |
| Floor 3 | | |
| Floor 2 | | |
| Floor 1 | | |
· U and V live on the consecutively numbered floor both higher number than the floor on which M and N lives.
· X and V like the same colour, while T likes different colour.
· O likes Green colour and lives on the floor which is preceded by two empty floors.
· U, V and X like the same colour i.e. Red (because if O likes green colour and there are only three people who like green colour), where X lives on the bottommost floor among all three.
· As, T likes Green colour so M and N likes Red colour.
· So, T, S and O like green colour, where O likes at the bottommost floor between three of them.
| Like Green colour (Case 1) | Like Green colour (Case 2) |
| S | T |
| T | S |
| O | O |
| Like Red colour order of living |
| U |
| V |
| M |
| N |
| X |
| | |
· M and N live on the consecutively numbered floor in increasing number respectively.
· U and V live on the consecutively numbered floor in increasing number respectively.
· T lives above X floor.
· X lives on the floor which is preceded by exactly one empty floor.
· So, Bottommost floor i.e. Floor 1 is an empty/vacant floor.
· So, there are two floors vacant between the people who like Red and Green colour cluster.
· Red is followed by Green is followed by Blue.
· So, two cases are possible i.e. Case 1 and Case 2.
Case 1:
| Floor | Person | Colour |
| Floor 16 | W | Blue |
| Floor 15 | R | Blue |
| Floor 14 | Q | Blue |
| Floor 13 | P | Blue |
| Floor 12 | Vacant | |
| Floor 11 | S | Green |
| Floor 10 | T | Green |
| Floor 9 | O | Green |
| Floor 8 | Vacant | |
| Floor 7 | Vacant | |
| Floor 6 | U | Red |
| Floor 5 | V | Red |
| Floor 4 | M | Red |
| Floor 3 | N | Red |
| Floor 2 | X | Red |
| Floor 1 | Vacant | |
Case 2:
| Floor | Person | Colour |
| Floor 16 | W | Blue |
| Floor 15 | R | Blue |
| Floor 14 | Q | Blue |
| Floor 13 | P | Blue |
| Floor 12 | Vacant | |
| Floor 11 | T | Green |
| Floor 10 | S | Green |
| Floor 9 | O | Green |
| Floor 8 | Vacant | |
| Floor 7 | Vacant | |
| Floor 6 | U | Red |
| Floor 5 | V | Red |
| Floor 4 | M | Red |
| Floor 3 | N | Red |
| Floor 2 | X | Red |
| Floor 1 | Vacant | |
S likes Green colour.
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