Four 4's Puzzle

Date: 10/24/2001 at 20:44:47
From: Ashley
Subject: Math trick

How can you get 73 by using 4 fours using any mathematical equation?  
I have been trying for two years on this.

Date: 10/25/2001 at 02:08:43
From: Doctor Jeremiah
Subject: Re: Math trick

Hi Ashley,

An Internet search yielded these pages:

   FAQ for the Four Fours mathematical puzzle - Peter Karsanow
   http://www.geocities.com/TimesSquare/Arcade/7810/44sfaq.htm   

   comp-sci Four Fours
   http://www.comp-sci.demon.co.uk/FourFours.html   

   Four Fours Problem - Paul Bourke
   http://astronomy.swin.edu.au/pbourke/fun/4444/   

   sci.math thread
   http://www.math.niu.edu/~rusin/uses-math/games/krypto/4fours   

All of them tell how to do 73. In fact all of them show how to do all 
numbers from 1 to 100.


This formula, where you stick in n square roots where it says 
   sqrt(sqrt(...(sqrt(
will give you the number n, and it only uses 4 fours (it came from the 
last page above):

log[log(4)/log(sqrt(sqrt(...(sqrt( [sqrt(4)*sqrt(4)] ))...)))]/
log(sqrt(4))

Probably the best ones for 73 were:
                    _         _
   (4! + 4! + sqrt(.4))/sqrt(.4)

where the two .4 in the square roots have a "repeating decimal bar" 
just above them, and
                                   _
   sqrt(sqrt(sqrt(4^(4!)))) + 4 / .4

where the .4 at the end has a "repeating decimal bar" just above it.


See also Ruth Carver's Four 4's Puzzle for the Math Forum:

   http://mathforum.org/ruth/four4s.puzzle.html   

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