
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion 
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May 12th, 2018, 12:35 AM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 310 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, 02:37 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894  Those are NOT 'rules' that need to be followed. They are just statements about the initial situation.

May 12th, 2018, 05:10 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 19,521 Thanks: 1747 
Below is an alternative arrangement, where the correct choice is (3) instead. Seated.PNG 
May 12th, 2018, 05:20 AM  #4  
Senior Member Joined: May 2008 Posts: 290 Thanks: 76  Beer soaked ramblings follow. Quote:
 
May 12th, 2018, 06:42 AM  #5  
Senior Member Joined: May 2016 From: USA Posts: 1,126 Thanks: 468  Quote:
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, 08:27 AM  #6 
Global Moderator Joined: Dec 2006 Posts: 19,521 Thanks: 1747 
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, 08:39 AM  #7  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,119 Thanks: 913  Quote:
Sir Jonah, agree with you that it is a thoughtprovoking, 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, 08:43 AM  #8 
Global Moderator Joined: Dec 2006 Posts: 19,521 Thanks: 1747 
My arrangement also satisfies the condition that U does not sit next to P, S or T.

May 12th, 2018, 10:59 AM  #9 
Senior Member Joined: May 2016 From: USA Posts: 1,126 Thanks: 468  

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