# Puzzle Questions with Answers — Floor, Box and Scheduling

> Puzzle questions with answers: floor, box and scheduling puzzles solved with a grid, the order to use the clues in, and how to handle two cases.

Source: https://www.sansal.in/aptitude/puzzles · Last updated: 2026-10-11 · How often it appears: High. Usually one puzzle set, with several questions built on the same arrangement.

A puzzle gives a handful of clues and asks several questions about one hidden arrangement. Almost all the time goes into building that arrangement; once the grid is complete, each question takes seconds. The skill being tested is the order in which you use the clues.

## Concepts

### Build one grid, then answer every question from it

Draw the grid before you look at the questions: one row for each fixed position (floor 1 to 5, Monday to Friday, box 1 at the bottom to box 5 at the top) and one column for each thing being placed. Fill a cell only when a clue forces it. A complete grid answers every question in the set; solving each question separately wastes the time the set is testing.

### Use the clues in order of how much they fix

Definite clues go in first ("Q is on floor 3"). Then tight links between two items ("immediately above", "the day after"), then gaps ("two floors between"), and negatives ("not on Monday") last, because they only remove options. If no clue is definite, start with the one that allows the fewest placements.

### Split into cases, and drop them fast

When a clue allows two or more placements, write each as its own row — Case 1, Case 2 — and carry all of them forward. Most cases break within one or two more clues. Never pick one case in your head and hope; that is how a whole set goes wrong.

### Read position words literally

"Above" means anywhere higher; "immediately above" means the next floor up. "Two floors between P and Q" means their floor numbers differ by 3, not 2. "Before Wednesday" means Monday or Tuesday only. Check which end is floor 1 or box 1 before you start.

## Formulas

| Formula | Rule | Note |
| --- | --- | --- |
| Grid layout | Rows = fixed positions (floors, days, months, box order); columns = what is being placed | Put position 1 at the bottom for floors and boxes, so the grid looks like the building or the stack. |
| Order of clues | Definite → immediately / the day after → gaps → negatives |  |
| Gap rule | n items between A and B → their positions differ by n + 1 | One floor between P and Q, with P on floor 2, puts Q on floor 4. |
| Above vs immediately above | Above: any higher position. Immediately above: exactly one position higher. |  |
| Case split | Two possible placements → two rows; cross a row out at its first contradiction |  |
| Last-place rule | n items in n positions: once n − 1 are placed, the last one is forced |  |
| If two cases survive | Answer only what is the same in every surviving case | Check the asked fact in each case before marking it. |

## Worked examples

### Example 1

**Question:** Five people — P, Q, R, S and T — live on floors 1 to 5 of a building, one per floor (floor 1 is the lowest). There are two floors between P and S. T lives immediately above P. Q lives on an even-numbered floor. R does not live on floor 1. Who lives on floor 3?

**Solution:**

1. No clue is definite, so start with the one that allows the fewest placements. "Two floors between P and S" means their floors differ by 3: (P, S) = (1, 4), (4, 1), (2, 5) or (5, 2).
2. T is immediately above P, so P cannot be on floor 5. Three cases remain: P1-T2-S4, S1-P4-T5 and P2-T3-S5.
3. Case P1-T2-S4: floors 3 and 5 are left for Q and R, and neither is even. Q has nowhere to go, so this case fails.
4. Case S1-P4-T5: floors 2 and 3 are left. Q takes the even floor 2 and R takes 3.
5. Case P2-T3-S5: floors 1 and 4 are left. Q takes 4, which leaves R on floor 1 — not allowed, so this case fails.
6. Only one case survives. From floor 1 up: S, Q, R, P, T.

**Answer:** R lives on floor 3

**Check:** Re-read every clue against S, Q, R, P, T: P (4) and S (1) have floors 2 and 3 between them; T (5) is directly above P; Q is on 2; R is on 3, not 1.

### Example 2

**Question:** Four boxes — Red, Blue, Green and Yellow — are stacked one above another, positions 1 (bottom) to 4 (top). Each holds a different item: books, cups, pens or toys. The Green box is at the top. The books are in the box immediately below the Green box. The Red box is somewhere below the Blue box. The toys are in the Red box. The cups are in the box immediately below the toys. What does the Yellow box contain?

**Solution:**

1. Draw a four-row grid with position 4 at the top, and two columns: colour and item.
2. Definite clues first: Green is at 4, so the books are at 3.
3. Box 3 holds books, so it is not Red (Red holds the toys). Red is not at 1 either, because the cups must sit directly under the toys. So Red is at 2 with the toys, and the cups are at 1.
4. Blue must be above Red, and the only free position above 2 is 3. Blue is at 3, holding the books.
5. Yellow takes the only position left, 1. The last item, pens, goes in the Green box.

**Answer:** The Yellow box contains the cups

**Check:** Full grid from the bottom: Yellow–cups, Red–toys, Blue–books, Green–pens. Every clue holds.

### Example 3

**Question:** Five trainees — Kavya, Latha, Mohan, Nikhil and Pooja — each give one presentation, on different days from Monday to Friday. Mohan presents on the day immediately after Latha. Two people present between Kavya and Mohan. Nikhil presents on an earlier day than Latha. Pooja presents on a later day than Mohan. Who presents on Tuesday?

**Solution:**

1. Number the days 1 (Monday) to 5 (Friday). Start with the tightest clue: Latha and Mohan on consecutive days gives (1, 2), (2, 3), (3, 4) or (4, 5).
2. Two people between Kavya and Mohan means their days differ by 3. Mohan on day 3 is impossible (Kavya would be on day 0 or 6). Three cases remain: L1-M2-K5, K1-L3-M4 and K2-L4-M5.
3. Nikhil is earlier than Latha, so Latha cannot be on Monday. Case L1-M2-K5 fails.
4. Pooja is later than Mohan, so Mohan cannot be on Friday. Case K2-L4-M5 fails.
5. Only K1-L3-M4 survives. Days 2 and 5 are left: Nikhil must be before Latha, so he is on day 2, and Pooja is on day 5.

**Answer:** Nikhil presents on Tuesday (the full order is Kavya, Nikhil, Latha, Mohan, Pooja)

**Check:** Mohan (Thursday) follows Latha (Wednesday); Nikhil and Latha sit between Kavya (Monday) and Mohan; Nikhil is before Latha; Pooja (Friday) is after Mohan.

## Practice questions

1. P, Q, R and S live on floors 1 to 4 of a building, one per floor (floor 1 is the lowest). R lives on the top floor. Q lives immediately above S. P does not live on floor 1. Who lives on floor 2?
   - A. P
   - B. Q
   - C. R
   - D. S
   - **Answer:** B. Q — R is on 4. Q and S need two consecutive floors among 1, 2 and 3: either S1-Q2 or S2-Q3. In the second case P would be left with floor 1, which is not allowed. So S is on 1, Q on 2 and P on 3.

2. J, K, L, M and N live on floors 1 to 5, one per floor (floor 1 is the lowest). J lives on an even-numbered floor, and L lives immediately above J. Two people live between K and L. N lives on a lower floor than M. Who lives immediately below J?
   - A. K
   - B. L
   - C. M
   - D. N
   - **Answer:** C. M — J is on 2 or 4 with L directly above: J2-L3 or J4-L5. Two people between K and L means their floors differ by 3; with L on 3, K would be on 0 or 6, which is impossible. So J is on 4, L on 5 and K on 2. N and M take floors 1 and 3 with N lower, so M is on 3, directly below J.

3. Five boxes — Red, Blue, Green, Black and White — are kept one above another. The Green box is at the top. The Blue box is immediately above the White box. Exactly one box is kept between the Red box and the White box. The Black box is somewhere below the Red box. Which box is immediately below the Red box?
   - A. Blue
   - B. White
   - C. Black
   - D. Green
   - **Answer:** A. Blue — Number the positions 1 (bottom) to 5 (top); Green is on 5. White and Blue take W1-B2, W2-B3 or W3-B4, and Red is two places from White: R3, R4 or R1 respectively. Black must be below Red. With R1 nothing is below Red; with R3 the only free position is 4, above Red. So W2-B3-R4 with Black on 1. Blue (3) is directly below Red (4).

4. Five departments — CSE, ECE, EEE, Mech and Civil — hold their fests on different days from Monday to Friday. ECE's fest is on Wednesday. Civil's fest is on the day immediately after Mech's. EEE's fest is on an earlier day than CSE's. Whose fest is on the day immediately before CSE's?
   - A. ECE
   - B. Mech
   - C. Civil
   - D. EEE
   - **Answer:** D. EEE — With ECE on Wednesday, Mech and Civil take Monday–Tuesday or Thursday–Friday. If they take Monday–Tuesday, EEE and CSE take Thursday and Friday in that order. If they take Thursday–Friday, EEE and CSE take Monday and Tuesday. Two arrangements survive, but in both EEE is the day before CSE, so the answer is fixed.

5. V, W, X, Y and Z each visit a client in a different month, from January to May of the same year. X visits in a month that has exactly 30 days. Y visits in the month immediately after W. W does not visit in January. Z visits in an earlier month than V. Who visits in May?
   - A. W
   - B. Y
   - C. Z
   - D. V
   - **Answer:** D. V — Of January to May, only April has 30 days, so X is in April. W and Y need consecutive free months among January, February, March and May: January–February or February–March. W is not in January, so W is in February and Y in March. Z and V take January and May with Z earlier, so V is in May.

6. Five boxes — P, Q, R, S and T — have different weights. Q is heavier than P but lighter than T. R is heavier than T. S is the lightest of all. Which box is the second heaviest?
   - A. T
   - B. R
   - C. Q
   - D. P
   - **Answer:** A. T — Chain the comparisons: P < Q < T, and T < R, so P < Q < T < R. S is the lightest, so the order from lightest is S, P, Q, T, R. R is the heaviest and T is second.

7. Four teachers — P, Q, R and S — give one lecture each, on different days from Monday to Thursday, and each teaches a different subject: Maths, Physics, Chemistry or English. Physics is on Tuesday. R lectures on Thursday. P teaches Maths, on the day immediately after Physics. S does not teach Physics. Chemistry is not on Monday. Which subject does R teach?
   - A. English
   - B. Maths
   - C. Chemistry
   - D. Physics
   - **Answer:** C. Chemistry — Physics is on Tuesday, so P's Maths lecture is on Wednesday. R is on Thursday, which leaves Monday and Tuesday for Q and S. S does not teach Physics, so S is on Monday and Q teaches Physics on Tuesday. English and Chemistry remain for Monday and Thursday; Chemistry is not on Monday, so R teaches Chemistry.

8. P, Q, R, S and T live on floors 1 to 5, one per floor (floor 1 is the lowest). T lives on floor 2. R lives immediately above P. P lives somewhere above Q. Q does not live on floor 1. How many people live between S and P?
   - A. 1
   - B. 2
   - C. 3
   - D. None
   - **Answer:** B. 2 — P and R need two consecutive free floors with R on top: P3-R4 or P4-R5. If P is on 3, floors 1 and 5 are left; Q cannot be on 1, so Q would be on 5 — above P, which is not allowed. So P is on 4 and R on 5. Q is below P and not on 1, so Q is on 3 and S is on 1. Between S (1) and P (4) live T and Q: 2 people.

## Where marks get lost

- Answering each question from scratch instead of completing one grid for the whole set.
- Reading "above" as "immediately above", or "two floors between" as a difference of 2.
- Following only one case of a clue that allows two placements.
- Answering from one surviving case when another surviving case gives a different answer.

## Related topics

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