A, B, C, D, E and F live on six different floors of the same building. The lowermost floor in the building is numbered 1, the floor above it, number 2 and so on till the topmost floor is numbered 6. D lives on an odd numbered floor but not 3. The sum of floors on which A and D live is 4. Only 3 people live between C and E. F lives immediately above B. The sum of floors on which B and C live is 10. What is the sum of floors on which A and E live?
5
D is on an odd floor other than 3, so D = 1 or 5. Since A + D = 4, D = 5 would give A = –1, which is impossible. So D = 1 and A = 3.
Only 3 people between C and E means their floors differ by 4: the pairs (1, 5) or (2, 6). Floor 1 is taken by D, so C and E are on floors 2 and 6 in some order.
B + C = 10: if C = 2, then B = 8, which is impossible; so C = 6, B = 4 and E = 2. F lives immediately above B, so F = 5.
| Floor | 6 | 5 | 4 | 3 | 2 | 1 |
| Person | C | F | B | A | E | D |
Therefore A lives on floor 3 and E on floor 2, so the required sum = 3 + 2 = 5.
Check: D (1) is odd and not 3; A + D = 3 + 1 = 4; between E (2) and C (6) live A, B and F, i.e. 3 people; F (5) is just above B (4); B + C = 4 + 6 = 10 – all conditions hold.
Hence, 5.
Similar Questions
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Important Questions from Floor Puzzle
If T joined P, Q, R and S, and T was on the third step, and Q was on a higher step than T, which step must be vacant?
If there are two steps in between the steps on which A and D are standing and C is standing on Step 6, A must be standing on which of the following steps?
If D is standing on step 1, on which step A could be standing?
If E sits in his office and faces the corridor, whose office is to his left?
- I, J, K, L, M and Y live on six different floors of the same building. The lowermost floor in the building is numbered 1, the floor above it, number 2 and so on, till the topmost floor is numbered 6. Only L lives above Y. I lives on some floor below J. Only M lives below K.
How many people live between J and M?
