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 May 12th, 2018, 01:35 AM #1 Senior Member   Joined: Aug 2014 From: India Posts: 343 Thanks: 1 How can we remove T or S and replace.... P, Q, R, S and T sit around a table. P sits two seats to the left of R and Q sits two seats to the right of R. If a new person U joins the group such that the initial conditions for the seating arrangement should be observed and also a new condition that U does not sit next to P, S or T be satisfied, then who will be the neighbours of P (one of the either side)? 1) S and T 2) S and Q 3) T and R 4) R and Q 5) U and T Solution: We create a new slot for the sixth person But since U will not sit next to P,S,T he will have to sit between R and Q. The arrangement will then look as follows: As we can see from the diagram the neighbors of P will be T and S. Choice is (1). My doubt: How can we remove T or S and replace with U if we clearly violating the rule: "P sits two seats to the left of R and Q sits two seats to the right of R"?
May 12th, 2018, 03:37 AM   #2
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Quote:
 Originally Posted by Ganesh Ujwal My doubt: How can we remove T or S and replace with U if we clearly violating the rule: "P sits two seats to the left of R and Q sits two seats to the right of R"?
Those are NOT 'rules' that need to be followed. They are just statements about the initial situation.

 May 12th, 2018, 06:10 AM #3 Global Moderator   Joined: Dec 2006 Posts: 20,271 Thanks: 1959 Below is an alternative arrangement, where the correct choice is (3) instead. Seated.PNG
May 12th, 2018, 06:20 AM   #4
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Beer soaked ramblings follow.
Quote:
 Originally Posted by Ganesh Ujwal P, Q, R, S and T sit around a table. P sits two seats to the left of R and Q sits two seats to the right of R. If a new person U joins the group such that the initial conditions for the seating arrangement should be observed and also a new condition that U does not sit next to P, S or T be satisfied, then who will be the neighbours of P (one of the either side)? 1) S and T 2) S and Q 3) T and R 4) R and Q 5) U and T Solution: We create a new slot for the sixth person But since U will not sit next to P,S,T he will have to sit between R and Q. The arrangement will then look as follows: As we can see from the diagram the neighbors of P will be T and S. Choice is (1). My doubt: How can we remove T or S and replace with U if we clearly violating the rule: "P sits two seats to the left of R and Q sits two seats to the right of R"?
Solved. Thank you for that thought-provoking, intellectually invigorating mental exercise.

May 12th, 2018, 07:42 AM   #5
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Quote:
 Originally Posted by skipjack Below is an alternative arrangement, where the correct choice is (3) instead. Attachment 9707
Skip

In your arrangement, Q is three to the left of P.

The relative placements of Q and R are fixed at - 2 and + 2. That leaves three choices for positions - 1 and + 1, namely S, T, and U, but U is not permitted in either of those position. The only freedom is the placement of S to right or left of P. Once that is done, all is determined.

 May 12th, 2018, 09:27 AM #6 Global Moderator   Joined: Dec 2006 Posts: 20,271 Thanks: 1959 You seem to have misread something. The requirement is that P sits two seats to the left of R and Q sits two seats to the right of R, both of which are true in the arrangement I gave. It's reasonable to assume that the people seated at the table are all facing the table, so that "to the left of" means "clockwise from" "and "to the right of" means "anticlockwise from" in relation to the diagram.
May 12th, 2018, 09:39 AM   #7
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Quote:
 Originally Posted by jonah Beer soaked ramblings follow. Thank you for that thought-provoking, intellectually invigorating mental exercise.
Coffee soaked ramblings follow.
Sir Jonah, agree with you that it is a thought-provoking, intellectually invigorating mental exercise.
Had me losing sleep...however, I suddenly was touched by the
"Round Table Angel" and clearly saw the ultimate solution:
now that we have 6 (after arrival of Mr. U) partakers, get the waiter
to rearrange the damn circular arrangement to an evenly spaced
6 "ass spots", and 99.9% of the problems are eliminated...

 May 12th, 2018, 09:43 AM #8 Global Moderator   Joined: Dec 2006 Posts: 20,271 Thanks: 1959 My arrangement also satisfies the condition that U does not sit next to P, S or T.
May 12th, 2018, 11:59 AM   #9
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Quote:
 Originally Posted by skipjack My arrangement also satisfies the condition that U does not sit next to P, S or T.

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