7
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Ten people are sitting around a circular table according to the following conditions:

  • There are two persons between X and U.
  • Y is neither adjacent to X nor opposite T.
  • P and T are adjacent to W.
  • Q is opposite S who is to the right of V.
  • R and W have four persons between them.
  • There are two persons between R and V.

Find the relative positions of each person. A diagram is preferable.


Source: TIME.com

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Since I am unable to upload images (don't know why), assume that the circle is a rectangle

So, from condition (III), we get (Let % = Other People and # = Blank Space)

P W T
% # %
% # %
% % %
As P and T are adjacent to W

Then, from condition (V),

P W T
% # %
% # %
% R %
As there are supposed to be 4 persons between R and W

After that, from condition (VI), we see that there are 2 possibilities :

No. 1
P W T
V # %
% # %
% R %
OR
No. 2
P W T
% # V
% # %
% R %

Now, with condition (IV), possibility No. 2 can be eliminated (Big thanks to @Alconja for telling me)

As S is supposed to be the right of V which is not possible in No. 2. Hence, we continue with No.1
P W T
V # Q
S # %
% R %

Then, with condition (I) and (II), we see that there are 2 possibilities again :

No.1
P W T
V # Q
S # X
U R Y
OR
No. 2
P W T
V # Q
S # U
X R Y

Since, Y is not adjacent to X,

No. 2 is the only possibility

So, the final answer is

P W T
V # Q
S # U
X R Y

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  • $\begingroup$ Your interpretation of "to the right" is inverted (usually it would be to the person's right, as they faced the centre of the table), which means * ends up opposite T, breaking rule (ii). $\endgroup$ – Alconja Oct 8 '18 at 4:43
  • $\begingroup$ hmm... lemme check @Alconja $\endgroup$ – Kevin L Oct 8 '18 at 4:52
  • $\begingroup$ @Alconja Thanks for telling me. Just edited the answer :D $\endgroup$ – Kevin L Oct 8 '18 at 4:57
  • $\begingroup$ how can you exclude that they are sitting in order T-W-P instead of P-W-T on the first line? $\endgroup$ – elias Oct 8 '18 at 13:31
  • $\begingroup$ Hmmm, true @elias $\endgroup$ – Kevin L Oct 8 '18 at 13:33
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The final configuration is:

   T Q U
 W       Y
 P       R
   V S X

Step by step solution (where an uppercase letter is a known position, and a lowercase is a possible position):

(iv) Q is opposite S who is to the right of V.

   . Q .
 .       .
 .       .
   V S .

(vi) There are two persons between R and V.
   r Q .
 .       .
 .       r
   V S .

(v) R and W have four persons between them.
   r Q .
 w       .
 .       r
   V S w

(iii) P and T are adjacent to W.
   pt Q .
 W       .
 pt      R
   V S .

(i) There are two persons between X and U.
   pt Q xu
 W       .
 pt      R
   V S xu

(ii) Y is neither adjacent to X nor opposite T.
   T Q U
 W       Y
 P       R
   V S X

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  • $\begingroup$ What the heck 8 seconds too late T_T $\endgroup$ – Kevin L Oct 8 '18 at 4:36
  • $\begingroup$ @KevinL - And I suspect we both spent more time fighting with the formatting than with the solving. :P $\endgroup$ – Alconja Oct 8 '18 at 4:40
  • $\begingroup$ Lol, exactly :D $\endgroup$ – Kevin L Oct 8 '18 at 4:51
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    $\begingroup$ The question is - what is considered "to the right" in a circle. I was looking from the center outwards, and got the same solution in the opposite order (if yours is considered clockwise, then mine is counter-clockwise). $\endgroup$ – Vilx- Oct 8 '18 at 8:29
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    $\begingroup$ @Vilx- It's to the person's right. Given that "ten persons are sitting around a circular table", I'd say it's a pretty safe bet that they're facing the centre (though yes, there is some ambiguity). $\endgroup$ – Alconja Oct 8 '18 at 9:11

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