# 10 people are sitting in two parallel rows with each row consisting of 6 seats, with one of the seats lying vacant in each row

While solving the question below, I have come up with two possibilities. The first one is the answer given. However, I am not finding any contradiction in the second possibility (all the statements given in the paragraph fit). Why is the second possibility wrong?

• Ten students are sitting in twelve seats in two parallel rows containing five students on each, in such a way that there is an equal distance between adjacent students.

• In row 1, students A, B, C, D and E are seated and all of them are facing south; in row 2, students P, Q, R, S and T are seated and all of them are facing north.

• One seat in each row is vacant. Therefore, in the given seating arrangement each member seated in a row faces another member of the other row.

• Each student has a different favorite subject i.e. Hindi, English, Sanskrit, Urdu, Art, Math, Science, Economics, Biology or Physics.

• Student A sits second-to-left of the student whose favorite subject is Hindi. Either A or the student whose favorite subject is Hindi sits adjacent to the extreme end position.

• T sits at one of the extreme ends of the row.

• There are three students sitting between T and S, whose favorite subject is English.

• The immediate neighbor of T faces B.

• One of the immediate neighbors of B faces R, whose favorite subject is Sanskrit.

• There are no vacant seats adjacent to R.

• C's favorite subject is Urdu and sits second to left of a vacant seat.

• One of the immediate neighbors of R is Q; one of the immediate neighbors of Q faces D.

• Q's favorite subject is Art; D's favorite subject is Math.

• The student whose favorite subject is Science sits immediately to the left of the student whose favorite subject is Economics.

• The student whose favorite subject is Biology sits three seats to the left of the student whose favorite subject is Physics.

In case you can't see the image, the two proposed solutions I have are:

[ ] [E] [C] [A] [B] [D]
[ ] [S] [P] [R] [Q] [T]


and

[E] [ ] [B] [C] [A] [D]
[T] [ ] [P] [R] [Q] [S]


Doesn't the line "there is an equal distance between adjacent students" indicate that the empty space must be at one of the extremes?

The distance between E and B in your second diagram is two seats, the distance between B and C is one seat. This violates the rule that "there is an equal distance between adjacent students"

• Yes, agreed. But in case the author meant that there was an equal distance between the adjacent "seats", then as hexomino has pointed out that the statement such as "The one whose favorite subject is Biology sits third to left of one whose favorite subject is Physics" could arise the argument that : in the second solution, A sits fourth(and not third) to the left of E by counting seats. So, should we consider seats or should we consider people while placing people? Mar 23, 2018 at 15:50
• I believe that it's normal to consider seats when working puzzles like this where vacant seats are a possibility. Where none of the seats are vacant, there is no conflict between counting seats and counting people. Mar 23, 2018 at 19:10

I think that it's to do with how some of the lines are interpreted.

For example, in the line,

The one whose favorite subject is Biology sits third to left of one whose favorite subject is Physics.

you could argue that, in the second solution, A sits fourth to the left of E, counting seats rather than people.

Also, looking at the line,

The immediate neighbour of T faces B

it could legitimately be argued that, in the second solution, the immediate neighbour of T is an empty seat.

• Yes, sir, this is the issue with this question. Whether to count seats or whether to count people. Mar 23, 2018 at 15:42