Use 2,3,7,8 to Write Math Expressions from 1 - 50

Date: 10/03/2004 at 11:46:16
From: ejae
Subject: using 2,3,7,8 find numbers 44 and 46

Using 2,3,7,8, find expressions for the numbers 44 and 46, such as
47 = (7 + 8) x 3 + 2.

I've tried all possible equations but can't figure out the right one.
I have done from 1 to 50 except these 2 numbers left.

Date: 10/05/2004 at 03:16:43
From: Doctor Korsak
Subject: Re: using 2,3,7,8 find numbers 44 and 46

Hello Ejae,

There is a neat free download PC program, 200Up, which generates all 
possible numbers using any specified four numbers.  You can download
it here:

    http://ourworld.compuserve.com/homepages/DavidandPenny/200Up.htm 

I just ran it for your case, and it got

   44 = (7*(3/2))*8

but it failed to get a representation of 22, 32, 42 and 46 when 
allowed to use only * / + - operators.  After adding the option of 
square roots, it got all but 22 and 46:

   32 = 2 * sqrt(7 - 3)*8
   42 = (3 / sqrt(2/8))*7

and then when I enabled using exponentiation x^y it got the rest of 
them:

   22 = sqrt(sqrt(7 - 2)^8 - 3
   46 = sqrt(7^(8/2)) - 3

Keep in mind that the idea behind this sort of assignment or challenge
is to give you practice in thinking mathematically.  Obviously, using
this software package removes much of that benefit.  But if you have
given a good effort and are stuck, it's a nice way to pick up those
last few numbers!

Please contact Dr. Math if you need further help.

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