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### Order of Operations Puzzle

```Date: 09/22/2002 at 23:25:04
From: Laurel
Subject: Order of operations puzzle

What is  _ + _ x _ - _ = 22?

We're given the numbers 2, 3, 4, 8.
```

```
Date: 09/24/2002 at 00:01:18
From: Doctor Ian
Subject: Re: Order of operations puzzle

Hi Laurel,

You're going to do the multiplication first, so the possible
multiplications are:

2*3 = 6
2*4 = 8
2*8 = 16
3*4 = 12
3*8 = 24
4*8 = 32

That means that the answer must be one of these:

__ +   6 - ___ = 22        use 4, 8

__ +   8 - ___ = 22        use 3, 8

__ +  16 - ___ = 22        use 3, 4

__ +  12 - ___ = 22        use 2, 8

__ +  24 - ___ = 22        use 2, 4

__ +  32 - ___ = 22        use 2, 3

This is a pretty common problem-solving technique: You replace one
hard problem with some easier ones.

Can you take it from here?

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Basic Algebra
High School Puzzles
Middle School Algebra
Middle School Puzzles

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