# Seating Arrangement

Eight sportsmen P, S, Q, R, U, B, J and C are sitting in a field,in a circle at equal distances. Three sportsmen on the circle are facing opposite side and other five are sitting facing the centre of the circle. S is sitting to the third right of B. R is not near to C. Q is sitting to the third left of R, who is second right of P and among these three players one is facing opposite to the centre of the circle. Two sportsmen are sitting between C and U and two are sitting between B and U. Q is sitting to the second left of J, who is facing the centre of the circle. S is facing the centre of the circle. U is not opposite to B and Q.

I have tried:

Drawn a circle point the equal distances 8 point in the circle

From the Data three facing outside and five sitting inside of the circle

First i took the data from which is facing inside and outside of the circle

J and S are facing centre of the circle ,then from these data i have point out s is sitting third to the right of B in the circle

I have a doubt - Q is sitting second to the left of J , we know J is facing center of the circle, According to J,Q is in which position?


Then we have to find another one, which is facing center? please anyone guide me how to solve the logical deduction for this question? Any help appreciated

The sportsmen are sitting in the following clockwise order:

C, P, B, R, J, U, Q and S. The sportsmen C, P and U are looking outwards.

Steps to solve this, where I've only spoiler-tagged the visual representations of the intermediate steps, because I'm lazy:

In order to know what a statement like "A sits to the left of B" means, we must know which way B is facing. When B faces inwards, to the left means clockwise; when B faces outwards, to the left means anticlockwise.

Q is sitting to the second left of J, who is facing the centre of the circle.

This is our starting point, because it gives two positions and one looking direction. We place J and Q on the circle. The dot marks where a person is looking:

                 1
8         2

Q             3

6    ·    4
J

Two sportsmen are sitting between C and U and two are sitting between B and U and U is not opposite to B and Q.

C, U and B form a V shape across the circle. U can't be in 2, because the two places with two persons between them are already taken by J and Q. U can't be in 3, because U isn't opposite to Q.

The only possible positions for U are 1 and 6 and there's no immediate way of telling which is valid. So let's lock the solution here (✻) and go with 1:

                 U
8         2

Q             3

6    ·    4
cb      J     cb

S is sitting to the third right of B.

That means B is in 6, because U and Q take up the places three to the left and right from 4. That also means that S is in 3 and that B is looking inwards. That and

S is facing the centre of the circle.

gives:

                 U
8         2

Q            ·S
·
B    ·    C
J

Q is sitting to the third left of R, who is second right of P and among these three players one is facing opposite to the centre of the circle.

R and P are in 2 adn 8 respectively. R is facing outwards, and so is P. But we're told that only one of them faces outwards, so this in an invalid arrangement.

Rewind to (✻) and place U in 6:

                cb

1
8         2

Q             3  cb

U    ·    4
J

R is not near to C and Q is sitting to the third left of R.

Only positions 2, 4 and 8 are still available. R is three positions away from Q and must be in either 2 o 4. The only way that R is not sitting next to C is that C is in 1 and R is in 4:

                 C
8         2

Q             B

U    ·    R
J

S is sitting to the third right of B and S is facing the centre of the circle.

This means that S sits in 8 and that B faces inwards. And S faces inwards as explicitly told in the second sentence.

Q is sitting to the third left of R, who is second right of P and among these three players one is facing opposite to the centre of the circle.

Now we can determine which way R and P are looking: R looks inwards and P looks outwards. Because only one of the three looks outwards, Q must look inwards.

Now we have established all five inward-looking sportsmen: S, B, R, J and Q. That means that the two sportsmen U and C, whose looking direction we don't know yet, look outwards.

Now in the last steps, the solution feel into place very quickly:

                 ·
C     ·
S         P
·
Q·           ·B
·
U    ·    R
·     J

(The statement that U isn't opposite to B is vacuous in the context of this puzzle, because that woul mean U and B hadthree people between them, but it is explicitly stated that they have only two between them. Perhaps this was meant to say U isn't opposite to J and Q, which would have made solving this straightforward.)

• @M Oehm In order to know what a statement like "A sits to the left of B" means, we must know which way B is facing. When B faces inwards, to the left means clockwise; when B faces outwards, to the left means anticlockwise. Mar 21 '17 at 17:30
• @Learninguser: Do you have a question about the passage you've quoted? Is it not clear that left and right have different meanings when facing inwards or outwards, because they are relative directions? Mar 21 '17 at 17:40
• yeah I have a Question @M Oehm we can continue in chat Mar 21 '17 at 17:43
• @M Oehm can you please join in this room chat.stackexchange.com/rooms/55493/… Mar 21 '17 at 17:45