Six persons A, B, C, D, E and F are standing in a circle. B is between F and…

Concept — In a circular arrangement, a clue of the form “X is between Y and Z” fixes a block of three consecutive seats: X sits in the middle and Y and Z are X's two neighbours, although which of them lies on which side is not yet decided. When such blocks together account for every person in the circle, the only freedom left is how the blocks are joined end to end, and a further adjacency clue settles that joining.

Application — Build the fixed blocks first, then decide how they join.

1. “B is between F and C” gives the block F–B–C, with B in the middle and F and C as its neighbours.

2. “A is between E and D” gives the block E–A–D, with A in the middle and E and D as its neighbours.

3. These two blocks use all six persons, so the circle is exactly the two blocks joined at both ends. That leaves only two circles: F–B–C–E–A–D back to F, or F–B–C–D–A–E back to F.

4. “F is to the left of D” places F in one of the two seats next to D. A circle can be read in either direction, so once F and D are neighbours the reading direction can always be chosen to put F on D's left; the working force of this clue is therefore that F and D must be adjacent. In F–B–C–D–A–E the neighbours of F are E and B, so D is not beside F and that circle is ruled out.

5. The circle is therefore F–B–C–E–A–D and back to F. Moving from A along the side that reaches F, the single seat in between is occupied by D.

Cross-check — Test all three clues against the circle F–B–C–E–A–D: B has F and C on either side, A has E and D on either side, and F and D are seated next to each other, so the circle can be read in the direction that puts F on D's left. Every clue holds, so the person seated between A and F is D.