DILR SET: Round Table Arrangement | Wide Arrangement | CAT 2025 DILR Slot 1 | Difficult
A round table has seven chairs around it. The chairs are numbered 1 through 7 in a clockwise direction. Four friends, Aslam, Bashir, Chhavi, and Davies, sit on four of the chairs. In the starting position, Aslam and Chhavi are sitting next to each other, while for Bashir as well as Davies, there are empty chairs on either side of the chairs that are sitting on.
The friends take turns moving either clockwise or counterclockwise from their chair. The friend who has to move in a turn occupies the first empty chair in whichever direction (s)he chooses to move. Aslam moves first (Turn 1), followed by Bashir, Chhavi, and Davies (Turns 2, 3, and 4, respectively). Then Aslam moves again followed by Bashir, and Chhavi (Turns 5, 6, and 7, respectively).
The following information is known.
1. The four friends occupy adjacent chairs only at the end of Turn 2 and Turn 6.
2. Davies occupies Chair 2 after Turn 1 and Chair 4 after Turn 5, and Chhavi occupies Chair 7 after Turn 2.
1. What is the number of the chair initially occupied by Bashir? ______
2. Who sits on the chair numbered 4 at the end of Turn 3? Options:
- Bashir
- Chhavi
- Davies
- No one
3. Which of the chairs are occupied at the end of Turn 6? Options:
- Chairs numbered 1, 2, 3, and 4
- Chairs numbered 1, 2, 6, and 7
- Chairs numbered 2, 3, 4, and 5
- Chairs numbered 4, 5, 6, and 7
4. Which of the following BEST describes the friends sitting on chairs adjacent to the one occupied by Bashir at the end of Turn 7? Options:
- Aslam and Chhavi
- Chhavi and Davies
- Davies only
- Chhavi only
Solutions Round Table Arrangement | Wide Arrangement | CAT 2025 DILR Slot 1 | Difficult
1. Correct Answer: 4. Reason: The starting constraints (A and C adjacent; B and D each with empty neighbours) combined with the fixed post-move facts (D at chair 2 after Turn 1, D at chair 4 after Turn 5, and C at chair 7 after Turn 2) produce a unique initial arrangement that satisfies all conditions: A = 6, B = 4, C = 7, D = 2. Any other initial placement for B forces a clash with the “adjacent after Turn 2 / Turn 6” conditions or the specified Davies positions. Hence Bashir starts at chair 4.
2. Correct Answer: No one. Reason: Using the valid move sequence, positions after Turn 3 are A = 1, B = 3, C = 6, D = 2. Davies moves into chair 4 only on Turn 4. Therefore at the end of Turn 3 chair 4 is empty; none of the four friends occupies it.
3. Correct Answer: chairs 4, 5, 6, and 7. Reason: After Turn 6 the positions are A = 7, B = 5, C = 6, D = 4. That set {4,5,6,7} is the contiguous block of four chairs required by the condition “adjacent only at end of Turn 6.” This matches the required adjacency and the computed move sequence.
4. Correct Answer: Davies only. Reason: At end of Turn 7 Bashir is at chair 5 in both valid end-states; his neighbours are chairs 4 and 6. Chair 4 is occupied by Davies, chair 6 is empty in both possible final placements for Chhavi (C ends at 1 or 3). Thus only Davies sits adjacent to Bashir.
Table Steps
Step 1: A and C must start on adjacent chairs, while B and D must each have empty chairs on both sides → forces C at 7 and A at 6 with D at 2 and B at 4. (Uses start-position rules.)
Step 2: Turn 1 requires Aslam to move to the first empty seat and Davies must occupy chair 2 after Turn 1 → A moves from 6 to 1, confirming D stays at 2. (From clue 2.)
Step 3: Turn 2 must end with all four friends in adjacent chairs → B must move from 4 to 3, giving occupied block 1–2–3–7. (Uses adjacency condition at end of Turn 2.)
Step 4: Chhavi must be at chair 7 after Turn 2 and must move on Turn 3 to the first empty chair → C moves from 7 to 6, making chair 4 empty. (From clue 2 and move rule.)
Step 5: Davies must reach chair 4 after Turn 5 → D moves at Turn 4 from 2 to 4 and remains there through Turn 5. (Clue 2.)
Step 6: Turn 6 must again produce four adjacent chairs → B moves from 3 to 5, forming block 4–5–6–7. (From adjacency condition at end of Turn 6.)
Step 7: Turn 7 movement by C can go to chair 1 or 3, but Bashir at 5 keeps only Davies adjacent at chair 4 → final adjacency answer fixed. (Uses Turn 7 placement requirement.)
These steps derive: B starts at 4; chair 4 is empty at end of Turn 3; chairs 4–5–6–7 are occupied at end Turn 6; only Davies is adjacent to Bashir at Turn 7.
Working Table
Chairs are numbered 1 to 7 clockwise.
Aslam = 6, Bashir = 4, Chhavi = 7, Davies = 2
Mover order: Turn1 A, Turn2 B, Turn3 C, Turn4 D, Turn5 A, Turn6 B, Turn7 C.
Each mover moves to FIRST empty seat in chosen direction.
Two valid direction sequences exist, but both produce identical positions at all key turns.
Below is the consolidated movement table (positions after each turn).
| Turn | Aslam (A) | Bashir (B) | Chhavi (C) | Davies (D) | Notes |
| Start | 6 | 4 | 7 | 2 | A & C adjacent; B & D have empty neighbors |
| 1 | 1 | 4 | 7 | 2 | A moves to chair 1; D must be at chair 2 after Turn1 ✔ |
| 2 | 1 | 3 | 7 | 2 | B moves to 3; all four become adjacent at end of Turn2 ✔ |
| 3 | 1 | 3 | 6 | 2 | C moves to 6; chair 4 is empty at end of Turn3 ✔ |
| 4 | 1 | 3 | 6 | 4 | D moves to 4 ✔ |
| 5 | 7 | 3 | 6 | 4 | A moves to 7; D is at 4 after Turn5 ✔ |
| 6 | 7 | 5 | 6 | 4 | B moves to 5; all four adjacent at Turn6 ✔ |
| 7 | 7 | 5 | 1 or 3 | 4 | C moves; both valid sequences give same adjacency outcome |
