Eight friends problem
Pretty hard problem that models could not solve a year ago
Prompt
Eight friends P,Q,R,S,T,V,W and Y are sitting around a square table in such a way that four of them sit at four corners of the square table while four of them sit in the middle of each of the four sides. The ones who sit at the four corners face the centre while those who sit in the middle of the sides face outside. S sits third to the right of P. P faces the centre. Y is not an immediate neighbor of P or S. T sits third to the right of R, who does not sit in the middle of any of the sides and also R is not an immediate neighbor of Y. Only one person sits between P and V. Q is not an immediate neighbor of V. Now. If all the persons are made to sit in the alphabetic order in clockwise direction starting from P, the positions of how many (excluding P) will remain unchanged as compared to their original seating positions?
