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### 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/
```
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