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...