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Old 2004-01-28, 20:14   #1
Neves
 
Jan 2004

616 Posts
Default 51 problem

Hello,

I'm looking for somebody that know this problem:

using four numbers 4 and the basic operations ( + - * / fatorial pow root ... )
find all number between 0 and 100
example:
0 = 4 + 4 - 4 - 4
1 = 44/44
2 = (4*4)/(4+4)
.
.
.
the really problem is to find the number 51.

does anybody knows this problem and where can I found more about?

sorry my english, I'm from Brazil.
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Old 2004-01-29, 06:04   #2
gbvalor
 
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Aug 2002

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Hello,

Assuming you can use double factorial n!!=n*(n-2)*(n-4)....

a solution is:

51 = 4! + 4! + 4!/4!!

I have to admit it stuck me a while.

Guillermo
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Old 2004-01-29, 10:56   #3
Neves
 
Jan 2004

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Are you a Math? or just curious as me?
I've never heard about double factorial. If it really exist, I'm sure it's is valid to use. Where can I found more about it?

what I'm really trying to found is a formal description of this problem, and a math/algorithm solution to found the answers.

congratulations due!!
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Old 2004-01-29, 12:02   #4
gbvalor
 
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Quote:
Are you Math? or just curious as me?
Just a Physicist (and Meteorologist) who likes math and programming.

About double factorial see

http://mathworld.wolfram.com/DoubleFactorial.html

Guillermo
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Old 2004-01-29, 18:14   #5
michael
 
Dec 2003
Belgium

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I see you can use sqrt(4)=41/2 can we use 42 too?

-michael
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Old 2004-01-29, 20:26   #6
Neves
 
Jan 2004

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41/2 is only and diferent representatio of sqrt(4).
if you found an other representation for any numbers but using only number 4, you can use it.
as I said before I just listen about this problem, I'm looking for help to found the origem of this. The correct propose.
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Old 2004-01-29, 20:38   #7
michael
 
Dec 2003
Belgium

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Then for instance F(sqrt(4)) * (4-4/4) =51 would be correct too?

F(2) is second Fermat number (or 22[sup]2[/sup]+1).

-michael

Last fiddled with by michael on 2004-01-29 at 20:40
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Old 2004-01-30, 11:13   #8
Maybeso
 
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Aug 2002
Portland, OR USA

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I like the all-factorial solution!!
But why stop at a paltry double factorial? Go for the tetrakaidecuple factorial!! (14-uple)

tetrakaidecuple factorial = n!!!!!!!!!!!!!! = n*(n-14)*(n-28)...

(sqrt(4)^4 + 4/4)!!!!!!!!!!!!!! = (2^4 + 1)!!!!!!!!!!!!!! = 17*3 = 51

You may want to limit the degree of factorial allowed, because too many numbers can be expressed with extreme factorials.
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Old 2004-01-30, 11:23   #9
michael
 
Dec 2003
Belgium

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What about this one

Pi(44-4!+4)=51

Pi(x) is amount of primes less or equal to x

-michael
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Old 2004-02-03, 06:58   #10
Uncwilly
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According to a book that I got with my TI-35:

Using 4 Fours and the following keys it is possible to build all whole numbers between 1 and 119.

+ - X / ( ) . ! ^2 =
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Old 2004-02-03, 09:38   #11
michael
 
Dec 2003
Belgium

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Strange that they say up to 119 cause 120 is a very easy number being 5!
(4+4/4)!=120

-michael
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