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Fun 7th grade Algebra problem

• To: mathgroup at smc.vnet.net
• Subject: [mg34731] Fun 7th grade Algebra problem
• From: johnnyturpin <johnnyturpin at earthlink.net>
• Date: Tue, 4 Jun 2002 03:41:41 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

I know this as the "four fours" problem, and I remember it from my 7th grade
Algebra class as an extra credit assignment, but recently it has been
entertaining all the puzzle solvers at my work. Being a 'C' programmer, I am
sure I could whip out a 'C' program to help solve this, but being new to
Mathematica I don't know where to start. Here is the problem:

Find the numbers 0 to 99 using any rational operator (i.e. an operation
which results in a rational number) and 4 fours, i.e., each equation must
contain no more or no less than 4 fours. Not all numbers may be possible.

Some examples:

0 = 4 + 4 - 4 - 4
1 = 4/4 + (4 -  4)
2 = 4/4 + 4/4
27 = 4! + 4/4 + sqrt(4)


The operators I remember to be valid (other than the obvious +, -, *, /
include:

() (Parenthesis for grouping)
! (factorial)
Sqrt ( square root)
X^y (exponent)

--- I am not sure about the following:
Min()
Max()
Floor()
Ceiling()

I am not sure if these can be thought of as "operators" and I don't remember
using them...




Ok, I realize that fundamentally factorial and square root include numbers
which are not fours (4 factorial = 4 * 3 * 2 * 1, and sqrt(4) = 4^1/2, but
for the sake of this puzzle, these can be thought of as integer operators
when applied to the number 4.

We are still working on 0 - 50 manually. 31 stumped us for several days...