Asha, Bina, Chitra, Deena, Ena, Fita, Gita, and Hema are sitting around a…

Concept

In a circular seating arrangement where everyone faces the centre, the left/right sense is reversed compared to arrangements where people face outward: moving to a person's right actually corresponds to the anticlockwise direction around the table, and moving to their left corresponds to the clockwise direction. So being k seats to the right of X means k seats anticlockwise from X, and k seats to the left of X means k seats clockwise from X. Fix one seat as a reference, translate every clue into a position equation (mod 8), and eliminate seats ruled out by the negative ("not a neighbour of") clues until a single consistent seating survives.

Application

1. Fix Fita's seat as position 0. Gita is third to the right of Fita, so Gita is at position 3 (right = anticlockwise, so 0 + 3 = 3).

2. Hema cannot be an immediate neighbour of Fita (so not at position 7 or 1) or of Gita (so not at position 2 or 4); of the remaining seats, only position 5 or position 6 stays open for Hema.

3. Asha sits second to the right of Hema. If Hema were at position 6, Asha would land at position 0 (6 + 2 = 8 ≡ 0), but that seat already belongs to Fita, so Hema must be at position 5, which puts Asha at position 7 (5 + 2 = 7).

4. Bina sits third to the right of Chitra, and Chitra cannot be an immediate neighbour of Gita (so not at position 2 or 4). Of the seats still open (1, 2, 4, 6), Chitra can only be at position 1 or position 6.

5. Testing Chitra at position 1 would put Bina at position 4 (1 + 3 = 4), leaving only positions 2 and 6 for Deena — but position 2 neighbours Chitra and position 6 neighbours Hema, and the next clue rules both out for Deena, so this branch collapses.

6. So Chitra must be at position 6, which puts Bina at position 1 (6 + 3 = 9 ≡ 1), leaving positions 2 and 4 open for Deena and Ena.

7. Deena cannot be an immediate neighbour of Hema (not position 4 or 6) or of Chitra (not position 5 or 7); of the two open seats, only position 2 satisfies this, so Deena takes position 2 and Ena takes the last open seat, position 4.

8. Asha is at position 7 and Ena is at position 4: the gap from Asha to Ena is 3 seats in the clockwise direction (7 → 6 → 5 → 4), and clockwise is the left-hand direction in this centre-facing arrangement, so Ena sits third to the left of Asha.

Cross-check

• Gita (3) is third to the right of Fita (0): 0 + 3 = 3.

• Hema (5) is not an immediate neighbour of Fita (0, neighbours 7 and 1) or of Gita (3, neighbours 2 and 4).

• Asha (7) is second to the right of Hema (5): 5 + 2 = 7.

• Bina (1) is third to the right of Chitra (6): 6 + 3 = 9 ≡ 1; Chitra (6) is not an immediate neighbour of Gita (3, neighbours 2 and 4).

• Deena (2) is not an immediate neighbour of Hema (5, neighbours 4 and 6) or of Chitra (6, neighbours 5 and 7).

• Every clue is satisfied by exactly one seating, which also matches the order shown in the reference diagram (clockwise from Asha: Asha, Chitra, Hema, Ena, Gita, Deena, Bina, Fita).

Result

So Ena sits third to the left of Asha.

Reference diagram of the final seating (viewed from above, everyone facing the centre):