SOLUTION: The marching band of Success University is practicing for a drill. Two hundred members equally spaced form a large circle and each member is numbered consecutively. What is the num

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Question 170709: The marching band of Success University is practicing for a drill. Two hundred members equally spaced form a large circle and each member is numbered consecutively. What is the number of the member who stands directly across from number 9?
I don't know if there is a formula for this or if it's something to do with 360 degrees of a circle. Thanks for the help.
Found 3 solutions by stanbon, scott8148, Mathtut:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The marching band of Success University is practicing for a drill. Two hundred members equally spaced form a large circle and each member is numbered consecutively. What is the number of the member who stands directly across from number 9?
I don't know if there is a formula for this or if it's something to do with 360 degrees of a circle.
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If #1 is at the 0 degree position, there are 201 spaces separating
the 200 members of the band.
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360/201 = 1.791044776 degrees separate each member from the next member.
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The 9th member is at position 9*1.791044776 = 16.11940299 degrees.
The member opposite the #9 position is at position 16.1194 + 180 degrees
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(16.1194 0299+ 180)/1.791044776 = 109.5
So the person opposite 9 is 110
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Cheers,
Stan H.

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
imagine the band arrayed in the circle

besides the two people directly across from each other, ther are 198 other band members

these 198 people will be evenly divided on either side of the circle between the two opposite people

half of 198 is 99, so there are 99 people between the opposites in either direction

if x is the number of one opposite, then you count 99 people plus the other opposite for a total of x+100

so 109 stands directly across from 9

Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
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%2Bt%2F2 if and only if x%3C=t%2F2 in our case 109=9+(200/2)
:
y=x+(t/2)-t or x-t%2F2 if and only if t%2F2%3Cx%3C=t eg 9=109-200/2