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.)
