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/