CAT 2025 Slot 1 · DILR · Set 3: Seven Chairs Around a Round Table

Davies first moves in Turn 4, so his position after Turn 1 is where he started — Chair 2.

Chhavi first moves in Turn 3, so her position after Turn 2 is also her starting chair — Chair 7.

Aslam starts next to Chhavi, so he began on Chair 1 or Chair 6.

Davies must have empty chairs on both sides, which means Chairs 1 and 3 were empty.

That rules out Chair 1 for Aslam, so Aslam began on Chair 6.

Bashir also needs empty chairs on both sides, and the occupied chairs so far are 2, 6 and 7.

Chair 3 fails because Chair 2 is taken, and Chair 5 fails because Chair 6 is taken.

Chair 4 works, with Chairs 3 and 5 both empty.

So Bashir started on Chair 4.

Shortcut. The two "isolated" friends do the work: Davies at Chair 2 immediately empties Chairs 1 and 3, which pins Aslam to Chair 6 and leaves Chair 4 as the only isolated seat remaining.

The starting arrangement is Aslam on 6, Bashir on 4, Chhavi on 7 and Davies on 2, with Chairs 1, 3 and 5 empty.

In Turn 1 Aslam moves clockwise to Chair 1 — Chair 7 is occupied, so the first empty chair that way is 1 — or counterclockwise to Chair 5.

Clue 1 requires all four to be adjacent at the end of Turn 2, which only works if Aslam goes to Chair 1.

Bashir then moves in Turn 2, counterclockwise to Chair 3, making the occupied chairs 7, 1, 2 and 3 — four in a row.

Chhavi moves in Turn 3 from Chair 7.

Going clockwise she would pass the occupied 1, 2 and 3 and land on Chair 4, leaving the four friends on Chairs 1, 2, 3 and 4 — adjacent again.

Clue 1 forbids adjacency at the end of Turn 3, so she must move counterclockwise to Chair 6.

Chair 4 is therefore empty at the end of Turn 3, and the answer is "No one" — the fourth option.

Shortcut. Clue 1 is a prohibition as much as a requirement. The clockwise move for Chhavi is the one that recreates a block of four, so the rule itself rules it out and sends her the other way.

At the end of Turn 3 the friends sit on Chairs 1 (Aslam), 2 (Davies), 3 (Bashir) and 6 (Chhavi).

Davies moves in Turn 4, and clue 2 puts him on Chair 4 after Turn 5 — but his only move before then is this one, so he must reach Chair 4 now.

Moving clockwise from Chair 2 he passes the occupied Chair 3 and lands on Chair 4, as required.

The occupied chairs are then 1, 3, 4 and 6.

Aslam moves in Turn 5, either clockwise to Chair 2 or counterclockwise to Chair 7.

Bashir then moves in Turn 6, and clue 1 requires all four to be adjacent afterwards.

If Aslam went to Chair 2, Bashir's options from Chair 3 are Chair 5 or Chair 1, giving \{2,4,5,6\} or \{1,2,4,6\} — neither is a run of four.

If Aslam went to Chair 7, Bashir moving clockwise from Chair 3 passes the occupied Chair 4 and lands on Chair 5.

That leaves Chairs 4, 5, 6 and 7 occupied — four consecutive chairs, as required.

The answer is the fourth option.

Shortcut. Clue 2 forces Davies to Chair 4 on his single available turn, which fixes the board before Turn 5. After that only two Aslam moves exist, and just one of them leaves Bashir able to close the block.

At the end of Turn 6 the friends are on Chairs 4 (Davies), 5 (Bashir), 6 (Chhavi) and 7 (Aslam).

Only Chhavi moves in Turn 7, and Bashir stays on Chair 5.

The chairs adjacent to Bashir are Chair 4 and Chair 6.

Chair 4 holds Davies, who does not move again.

Chair 6 is Chhavi's own chair, and she is about to leave it.

Moving clockwise from Chair 6 she passes the occupied Chair 7 and lands on Chair 1; moving counterclockwise she passes the occupied Chairs 5 and 4 and lands on Chair 3.

Both moves are allowed, since neither recreates a block of four, but either way Chhavi vacates Chair 6.

So Bashir's only neighbour is Davies, and the answer is "Davies only" — the third option.

Shortcut. Chhavi cannot stay put, so the seat on one side of Bashir empties whatever she chooses. That makes the answer independent of her direction, which is why the question can be answered even though her move is not determined.