
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion 
 LinkBack  Thread Tools  Display Modes 
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 
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, 06:10 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 19,887 Thanks: 1836 
Below is an alternative arrangement, where the correct choice is (3) instead. Seated.PNG 
May 12th, 2018, 06:20 AM  #4  
Senior Member Joined: May 2008 Posts: 297 Thanks: 81  Beer soaked ramblings follow. Quote:
 
May 12th, 2018, 07:42 AM  #5  
Senior Member Joined: May 2016 From: USA Posts: 1,192 Thanks: 489  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, 09:27 AM  #6 
Global Moderator Joined: Dec 2006 Posts: 19,887 Thanks: 1836 
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  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,486 Thanks: 950  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, 09:43 AM  #8 
Global Moderator Joined: Dec 2006 Posts: 19,887 Thanks: 1836 
My arrangement also satisfies the condition that U does not sit next to P, S or T.

May 12th, 2018, 11:59 AM  #9 
Senior Member Joined: May 2016 From: USA Posts: 1,192 Thanks: 489  

Tags 
remove, replace 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
MS Word grayed out "Replace All" is nonfunctional  Loren  Computer Science  5  December 24th, 2017 05:33 PM 
replace indicator functions with convex conjugates?  Azalea  Applied Math  0  February 27th, 2014 05:56 AM 
When do you replace x when finding f'(a) using the def?  Singularity  Calculus  3  October 25th, 2013 02:28 PM 
*solved it please remove  1101  Algebra  1  June 3rd, 2011 03:21 AM 