Logical Reasoningतार्किक क्षमता · मंज़िल और बॉक्स पहेलियाँ

Floor and Box Puzzlesमंज़िल और बॉक्स पहेलियाँ questions and answersप्रश्न और उत्तर

Floor puzzles put one person on each floor of a building and give clues such as “A lives immediately above B” or “two people live between C and D”. Box puzzles stack boxes instead of people, and the same method works for both.

Unlimitedअसीमित fresh questionsनए प्रश्न
Answersउत्तर always one tap awayहमेशा एक टैप दूर
1 subtopicउप-टॉपिक
IBPS PO ~5
TCS NQT ~1

Practice questions are in English for now.अभ्यास के प्रश्न अभी अंग्रेज़ी में हैं।

How floor and box puzzles worksमंज़िल और बॉक्स पहेलियाँ को समझिए

Draw the floors as a column of boxes numbered from 1 at the bottom to the top floor. Most papers number from the bottom; read the first line of the puzzle to confirm, because counting from the wrong end flips every answer.

Place the clues that fix a floor first: top, bottom, “on floor 3”, “on an even-numbered floor”. Then treat “immediately above” and “exactly k between” clues as blocks of fixed shape and try each position where the block fits.

When a block fits in two places, keep both columns side by side. Negative clues such as “does not live on an adjacent floor” and odd/even clues usually remove one of them within a line or two.

Tricks that save timeसमय बचाने वाली ट्रिक्स

All tricks →सभी ट्रिक्स →

Each trick says when to use it, why it works and when it fails. Formula tricks are checked by code over their whole range.हर ट्रिक बताती है कि उसे कब इस्तेमाल करें, वह क्यों काम करती है और कब नहीं। सूत्र वाली ट्रिक्स को कोड से उनकी पूरी रेंज पर जाँचा गया है।

Formulaसूत्रRarely taughtकम सिखाई जाने वाली✓ Checked on 44 cases✓ 44 मामलों पर जाँची गई

A gap clue fits in 2(n − k − 1) ways

Use it when:कब इस्तेमाल करें: A clue says exactly k people live between A and B and you want to know how many cases to draw.

The pair occupies floors f and f + k + 1, so f runs from 1 to n − k − 1.
Either person can be the lower one: double it.
If that number is large, place a more fixed clue first.

Exampleउदाहरण

Seven floors, exactly three people between A and B. How many placements?

→ 2 × (7 − 3 − 1) = 6.

Why it works, and when it failsयह क्यों काम करती है, और कब नहीं

Why:क्यों: Choosing the lower floor f fixes the upper floor at f + k + 1, which must be at most n, so there are n − k − 1 choices; swapping who is lower doubles them.

Limits:सीमाएँ: Counts placements of that one pair before any other clue is used.

Formulaसूत्र✓ Checked on 572 cases✓ 572 मामलों पर जाँची गई

People between floors p and q = |p − q| − 1

Use it when:कब इस्तेमाल करें: A floor or box puzzle asks how many people (or boxes) are between two others.

Find both floor numbers.
Subtract and take away 1.

Exampleउदाहरण

A is on floor 2 and B on floor 6. How many live between them?

→ 6 − 2 − 1 = 3 (floors 3, 4, 5).

Why it works, and when it failsयह क्यों काम करती है, और कब नहीं

Why:क्यों: The floors strictly between p and q are p + 1, …, q − 1, which is q − p − 1 floors, each with one person.

Limits:सीमाएँ: One person per floor. If a floor can hold two flats or people, count people, not floors.

Solved examplesहल किए गए उदाहरण

Answers and full solutions are shown. Hide them to test yourself first.उत्तर और पूरे हल दिखाए गए हैं। पहले खुद को परखने के लिए इन्हें छिपाइए।

Example 1उदाहरण 1 · Floor puzzles (one person per floor) · Easyआसान
5 friends (Rohan, Ayaan, Joseph, Ananya, Arjun) live in a 5-storey building in Nagpur, one on each floor. The bottom floor is floor 1 and the top floor is floor 5. • Rohan and Ananya do not live on adjacent floors. • Ananya lives immediately above Joseph. • Ayaan and Arjun do not live on adjacent floors. • Ayaan and Joseph do not live on adjacent floors. • Arjun lives on the top floor. • Joseph lives neither on the top floor nor on the bottom floor. Who lives on floor 4?
1. Arjun
2. Ananya
3. Rohan
4. Joseph
Answer:उत्तर: Ananya
1. The clues leave exactly one arrangement (floor 1 → 5): Ayaan, Rohan, Joseph, Ananya, Arjun.
2. Who lives on floor 4? → Ananya.
Example 2उदाहरण 2 · Floor puzzles (one person per floor) · Mediumमध्यम
6 friends (Vihaan, Rohan, Fatima, Aditya, Kabir, Ayaan) live in a 6-storey building in Jaipur, one on each floor. The bottom floor is floor 1 and the top floor is floor 6. • Exactly 4 people live between Rohan and Vihaan. • Rohan lives somewhere above Kabir. • Aditya lives exactly two floors above Vihaan. • Exactly 2 people live between Fatima and Ayaan. • Ayaan lives on an even-numbered floor. How many people live between Rohan and Ayaan?
1. 2
2. 3
3. 4
4. 5
Answer:उत्तर: 3
1. The clues leave exactly one arrangement (floor 1 → 6): Vihaan, Ayaan, Aditya, Kabir, Fatima, Rohan.
2. How many people live between Rohan and Ayaan? → 3.
Example 3उदाहरण 3 · Floor puzzles (one person per floor) · Hardकठिन
7 friends (Isha, Meera, Harpreet, Aarav, Joseph, Lakshmi, Diya) live in a 7-storey building in Indore, one on each floor. The bottom floor is floor 1 and the top floor is floor 7. • Isha lives exactly two floors above Harpreet. • Harpreet lives on an even-numbered floor. • Exactly one person lives between Isha and Joseph. • Aarav lives somewhere above Meera. • Isha lives immediately above Aarav. • Lakshmi lives exactly three floors above Isha. Who lives on floor 3?
1. Isha
2. Harpreet
3. Aarav
4. Diya
Answer:उत्तर: Aarav
1. The clues leave exactly one arrangement (floor 1 → 7): Meera, Harpreet, Aarav, Isha, Diya, Joseph, Lakshmi.
2. Who lives on floor 3? → Aarav.
Example 4उदाहरण 4 · Floor puzzles (one person per floor) · Mediumमध्यम
6 friends (Rohan, Harpreet, Isha, Tenzin, Aditya, Meera) live in a 6-storey building in Surat, one on each floor. The bottom floor is floor 1 and the top floor is floor 6. • Tenzin lives on an odd-numbered floor. • Harpreet lives neither on the top floor nor on the bottom floor. • Rohan lives immediately above Meera. • Aditya lives exactly three floors above Tenzin. • Harpreet lives somewhere above Tenzin. • Exactly one person lives between Harpreet and Tenzin. • Exactly 4 people live between Meera and Aditya. On which floor does Rohan live?
1. 1
2. 2
3. 3
4. 5
Answer:उत्तर: 2
1. The clues leave exactly one arrangement (floor 1 → 6): Meera, Rohan, Tenzin, Isha, Harpreet, Aditya.
2. On which floor does Rohan live? → 2.
Example 5उदाहरण 5 · Floor puzzles (one person per floor) · Mediumमध्यम
6 friends (Rohan, Aditya, Kabir, Vihaan, Ayaan, Isha) live in a 6-storey building in Lucknow, one on each floor. The bottom floor is floor 1 and the top floor is floor 6. • Aditya lives exactly three floors above Ayaan. • Aditya lives exactly two floors above Kabir. • Kabir lives exactly two floors above Vihaan. • Exactly one person lives between Rohan and Ayaan. • Isha lives immediately above Kabir. Who lives on floor 3?
1. Vihaan
2. Aditya
3. Ayaan
4. Kabir
Answer:उत्तर: Ayaan
1. The clues leave exactly one arrangement (floor 1 → 6): Rohan, Vihaan, Ayaan, Kabir, Isha, Aditya.
2. Who lives on floor 3? → Ayaan.
Example 6उदाहरण 6 · Floor puzzles (one person per floor) · Mediumमध्यम
6 friends (Arjun, Rohan, Vihaan, Ananya, Isha, Aarav) live in a 6-storey building in Nagpur, one on each floor. The bottom floor is floor 1 and the top floor is floor 6. • Isha lives neither on the top floor nor on the bottom floor. • Aarav lives on the bottom floor. • Arjun lives neither on the top floor nor on the bottom floor. • Ananya lives somewhere above Vihaan. • Rohan and Ananya do not live on adjacent floors. • Isha lives exactly three floors above Arjun. • Exactly one person lives between Rohan and Ananya. • Exactly 2 people live between Ananya and Vihaan. How many people live between Arjun and Isha?
1. 1
2. 2
3. 3
4. 4
Answer:उत्तर: 2
1. The clues leave exactly one arrangement (floor 1 → 6): Aarav, Arjun, Vihaan, Rohan, Isha, Ananya.
2. How many people live between Arjun and Isha? → 2.

Common mistakesआम गलतियाँ

Counting floors from the top when the puzzle numbers them from the bottom.
Reading “A lives above B” as “immediately above”.
Counting one of the two people themselves in “how many live between”.

Frequently asked questionsअक्सर पूछे जाने वाले प्रश्न

How many people live between floors 2 and 6?

Three: those on floors 3, 4 and 5. In general |p − q| − 1.

What is the difference between “above” and “immediately above”?

“Immediately above” means the very next floor up. “Above” only means somewhere higher, possibly several floors up.

Are box puzzles solved the same way?

Yes. Replace floors with positions in the stack and people with boxes; the clues and the block method are identical.