Seven people — Ishaan, Kavya, Meera, Nikhil, Pooja, Rohan and Tanvi — live in a seven-storey building, one on each floor, numbered 1 (the lowest) to 7 (the top). Each has a different favourite city: Delhi, Mumbai, Kolkata, Chennai, Jaipur, Pune and Lucknow. On the board, floor 1 is on the left and floor 7 on the right.
Conditions
Each floor has exactly one resident.
“Above” and “below” compare floor numbers: “immediately above” means exactly one floor higher, while “somewhere above” means any higher floor.
“The Delhi fan” means the person whose favourite city is Delhi, and so on for the other cities.
Clues
Meera lives on the floor immediately above Ishaan.
Exactly one person lives between Kavya and Ishaan.
Nikhil lives on an even-numbered floor somewhere below Ishaan.
Pooja's favourite city is Kolkata, and Pooja lives somewhere above Meera.
The Pune fan lives on floor 1.
The Delhi fan lives on the floor immediately below Kavya.
The Chennai fan lives exactly two floors above the Delhi fan.
The Mumbai fan lives on the floor immediately above the Lucknow fan.
Tanvi lives somewhere below Rohan.
Rohan lives somewhere below Ishaan, and Rohan's favourite city is not Chennai.
Question 1 · Multiple choice (+3 / −1)
Whose favourite city is Lucknow?
Show the solutionSolution
Answer: C. Ishaan
Ishaan lives on 5 and Meera on 6, leaving Mumbai, Lucknow and Jaipur for floors 3, 5 and 6.
The Mumbai fan is immediately above the Lucknow fan, so they are on 6 and 5: Ishaan likes Lucknow.
Question 2 · Type in the answer (+3 / 0)
How many people live between Rohan and Meera?
Show the solutionSolution
Answer: 3
Rohan lives on floor 2 and Meera on floor 6.
Kavya (3), Nikhil (4) and Ishaan (5) live between them: 3 people.
Question 3 · Multiple choice (+3 / −1)
Who lives on the floor immediately below the person whose favourite city is Chennai?
Show the solutionSolution
Answer: B. Kavya
The Delhi fan is on floor 2 (just below Kavya on 3), so the Chennai fan is on floor 4: Nikhil.
Floor 3, immediately below, belongs to Kavya.
Question 4 · Multiple choice (+3 / −1)
Which of the following is true?
Show the solutionSolution
Answer: D. Nikhil's favourite city is Chennai
A is false: Rohan (2) lives immediately below Kavya (3).
B is false: the Mumbai fan, Meera, lives on floor 6.
C is false: Tanvi likes Pune.
D is true: Nikhil, on floor 4, likes Chennai.
Question 5 · Type in the answer (+3 / 0)
How many people live above the person whose favourite city is Jaipur?
Show the solutionSolution
Answer: 4
Kavya, on floor 3, is the Jaipur fan.
Nikhil, Ishaan, Meera and Pooja live on floors 4 to 7: 4 people.
Full worked solution
Pooja is above Meera, who is immediately above Ishaan, so Ishaan lives on floor 5 at the highest. Nikhil is on an even floor below Ishaan, so Ishaan is on floor 3 at the lowest. Try Ishaan on 3, 4 and 5.
Try Ishaan on floor 3: Meera is on 4 and Nikhil, on an even floor below 3, is on 2. Rohan must be below Ishaan, so Rohan is on floor 1 — and then Tanvi has no floor below Rohan.
Try Ishaan on floor 4: Meera is on 5, Nikhil on 2, so Kavya (two floors from Ishaan) is on 6 and Pooja, above Meera, on 7. Rohan and Tanvi take floors 3 and 1, Tanvi lower. The Delhi fan, just below Kavya, is Meera on 5, so the Chennai fan would be on 7 — but Pooja likes Kolkata.
So Ishaan lives on floor 5, Meera on 6 and Pooja, above Meera, on 7 with Kolkata. Kavya is two floors from Ishaan, and floor 7 is taken, so Kavya is on 3. Nikhil is on 2 or 4.
Rohan and Tanvi both live below Ishaan, Tanvi lower. The free floors below 5 are 1 and whichever of 2 and 4 Nikhil leaves, so Tanvi is on floor 1 and likes Pune.
The Delhi fan lives just below Kavya, on floor 2, so the Chennai fan is on floor 4. Floors 2 and 4 belong to Rohan and Nikhil, and Rohan does not like Chennai: Rohan is on 2 with Delhi and Nikhil on 4 with Chennai.
Mumbai, Lucknow and Jaipur are left for floors 3, 5 and 6. The Mumbai fan is immediately above the Lucknow fan, which only floors 5 and 6 allow: Ishaan likes Lucknow, Meera Mumbai, and Kavya Jaipur. Everything is placed.