Pupil 47 Opposite Pupil 16 in the Circle

Date: 09/17/2002 at 18:26:24
From: Zachary Small
Subject: Math word problem

If, in Mr. Simmons' class, pupil 47 is opposite pupil 16 when the 
group is seated in a circle, how many students are in the class?

I am stuck. I have tried to do division, addition, subtraction, 
geometry, etc.

Zachary

Date: 09/18/2002 at 10:58:02
From: Doctor Ian
Subject: Re: Math word problem

Hi Zachary,

Let's make a drawing of the situation.  (When you don't know what 
else to do, that's often a good place to start.) 

                31 students 



    #16                                #47



         15 students      ? students
         \_________________________/
                31 students

If you go clockwise from student #16 to student #47, you have to pass 
by 31 students, right?  If they're on opposite sides of a 
circle, then you'd have to pass 31 more students in order to get 
all the way around to #16 again.  

This second group includes students #1 through #15... so how many 
_other_ students does it have to include?  And what does that 
tell you about the total number of students? 

Can you take it from here?

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/