Question 170709
starting with 1 as you move around you simply add 100(200/2) to whatever position you are referring to in order to get the persons number your standing directly across from. position 1 would be across from 101 and 2 would be across from 102, 100 would be across from 200.....so 9 would be across from 109.  A problem arise with this when you are trying to find the position across from anything above 100  101+100=201....and there is no position 201...
so a way to generalize this would be 
:
:
let x= the position in question
let y= the position directly across from x
let t= the total number of positions around a circle(t must be even for this to work.)
:
{{{y=x+t/2}}}  if and only if {{{x<=t/2}}} in our case 109=9+(200/2)
:
y=x+(t/2)-t or {{{x-t/2}}} if and only if {{{t/2<x<=t}}} eg 9=109-200/2