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### 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

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/

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.

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

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