Who sits where?

Eight persons A through H each of a different profession among engineer, doctor, teacher, policeman, singer, mechanic, painter and politician are sitting in a row of eight seats facing the dias. Their arrangement is as follows:

(i) Neither the teacher nor the policeman is sitting at the end.

(ii) The engineer is adjacent to H, who is fifth to the left of the painter.

(iii) The painter sits adjacent to G, the policeman, who sits fifth to the right of the engineer.

(iv) E, the politician sits in the fourth or fifth seat from either ends and is sitting to the immediate right of the mechanic.

(v) C is second to the right of the singer, who is exactly between the teacher and A.

(vi) F is exactly between B and the singer.

Source : time.com

• By "exactly between" does this mean that it can go B # F # Singer or B # # F # # Singer, as well as B F Singer? (Where # is an unknown seat) Commented Oct 11, 2018 at 13:56
• Yes..multiple cases are there.
– sam
Commented Oct 11, 2018 at 14:10

The Orientation is:

B H F E D G C A

Their Professions in order:

Engineer Teacher Mechanic Politician Singer Policeman Painter Doctor

Or as an image:

Method Part 1:

First of all, I took the second and third clues:
The engineer is adjacent to H, who is fifth to the left of the painter.
The painter sits adjacent to G, the policeman, who sits fifth to the right of the engineer.
And utilising "fifth to the right", determined that they could go into one configuration which took up 7 spaces, with a spare seat on either the left or the right.

Method Part 2:

Then, using the fourth clue:
E, the politician sits in the fourth or fifth seat from either ends and is sitting to the immediate right of the mechanic.
It's clear that there are two possibilities for the position of the Politician and the Mechanic, with the Politician either in seat 4 or 5, and the Mechanic either in seat 3 or 4.
Assuming the above set of 7 go 1 through 7 and the spare seat being in number 8 (worked out through trial and error), this gives us the following:

Method Part 3:

Next we use the fifth clue:
C is second to the right of the singer, who is exactly between the teacher and A.
One of the only places the Singer can go such that C is second to the right of it and there is room for the Teacher and A to be equal distance away either side of the Singer, is in the fifth seat, with A and Teacher placed as follows, meaning that the Mechanic and Politician take up seats 3 and 4.

Method Part 4:

Penultimately, we take clue six:
F is exactly between B and the singer.
Looking at the letters remaining to fill, F and B can only go to the left of Singer, with F in the middle, making:

And finally we can fill in the blanks with D and Doctor to get the final solution above.

– sam
Commented Oct 11, 2018 at 14:49
• How's that method for you? Commented Oct 11, 2018 at 15:24
• you didn't consider the case where Engineer is to the left of H ?
– sam
Commented Oct 11, 2018 at 19:20