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/
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.