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Old 2005-10-03, 22:06   #100
fetofs
 
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This thread is full of status updates, but could someone kindly enough provide a list of every number found smaller than 1000 in 1/4 or 2/4 time?
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Old 2005-10-04, 05:49   #101
R. Gerbicz
 
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"Robert Gerbicz"
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Hungary

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Default New solutions and program

Part 1.:
Here is a solution for famous 93 and a solution for 203:
93=((4!-4sqsq)sq-4sqsq)/(4!sq)
203=(4!sq-4sqsqsq)/(4sqsq-4!sq)

I've written an UBASIC program to find using fewest 4's ( no more than 4 )
formulas for n ( here 0<=n<1000 ). This program find solutions if intermediate values are such rationals where abs(denominator*numerator)<2^50 is true.
It took about 1 hour to compute these solutions ( on a P4 Celeron 1.7 GHz ).
I think it is very probably that remaining integers hasn't got solutions.

Program is in four4.txt and solutions in solution.txt ( integers up to 999 ).
There are formulas where program has found formulas using fewer 4's.
For example this pretty: 180=(4!/4)!/4 see solution.txt
( Some formulas has got some spare parentheses ).
Attached Files
File Type: txt solution.txt (21.6 KB, 265 views)

Last fiddled with by R. Gerbicz on 2005-10-04 at 05:53
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Old 2005-10-04, 05:51   #102
R. Gerbicz
 
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"Robert Gerbicz"
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Part 2.:
Here is the program in four4.txt
Attached Files
File Type: txt four4.txt (2.9 KB, 264 views)
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Old 2005-10-04, 12:27   #103
fetofs
 
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Bye bye 93!!!! I'll miss you!!!

But I can't use Gerbicz's program...
Will someone try to solve the other remaining ones?
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Old 2007-02-01, 19:30   #104
petrw1
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Quote:
Originally Posted by fetofs View Post
Bye bye 93!!!! I'll miss you!!!

But I can't use Gerbicz's program...
Will someone try to solve the other remaining ones?
Coming from the camp the squared is NOT valid since it uses a 2 ... I have solutions for all 101 from 0 - 100 including 93:

93 = (4!*4) - sqrt(4/.4~)
93 = 96 - 3
assuming .4~ is the repeating decimal that equates to .444444 OR 4/9.
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Old 2007-03-22, 01:06   #105
fetofs
 
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Sorry, but you can't simply modify the rules we've been playing by all along, that explictly allow squaring, forbid square roots and repeating decimals.
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Old 2016-10-20, 20:36   #106
R. Gerbicz
 
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"Robert Gerbicz"
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Up to n=10000 the number of missing values is 7116. Found for each possible n the formula that used the smallest number of 4 (up to four values), and in those sequences printed the shortest one ("shortest" in my own form).
Attached Files
File Type: txt fourfour.txt (83.7 KB, 281 views)
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Old 2021-05-04, 15:40   #107
petrw1
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Default If you love this kind of puzzle but can never get enough...

Look up this app:
TCHISLA
Russian for "numbers"

Asks you to solve for every number from 1 to 10,000
with the least number of each digit from 1 to 9
using only:
+ - X / !
Square root
Concatenation: 66 or 666 or 6666

For example here is a wild on for 41 with 4 4's:
SQRT(((4+4)!+(4)!)/(4)!)

Tchisla looks like an ordinary calculator but it is designed to help you in your fight with the problem. It proposes you autocomplete variants that can lead you to the goal. You choose the way and the app calculates and performs all the menial job for you.
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