20051003, 22:06  #100 
Aug 2005
Brazil
2·181 Posts 
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?

20051004, 05:49  #101 
"Robert Gerbicz"
Oct 2005
Hungary
5D6_{16} Posts 
New solutions and program
Part 1.:
Here is a solution for famous 93 and a solution for 203: 93=((4!4sqsq)sq4sqsq)/(4!sq) 203=(4!sq4sqsqsq)/(4sqsq4!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 ). Last fiddled with by R. Gerbicz on 20051004 at 05:53 
20051004, 05:51  #102 
"Robert Gerbicz"
Oct 2005
Hungary
2·3^{2}·83 Posts 
Part 2.:
Here is the program in four4.txt 
20051004, 12:27  #103 
Aug 2005
Brazil
101101010_{2} Posts 
Bye bye 93!!!! I'll miss you!!!
But I can't use Gerbicz's program... Will someone try to solve the other remaining ones? 
20070201, 19:30  #104  
1976 Toyota Corona years forever!
"Wayne"
Nov 2006
Saskatchewan, Canada
5·953 Posts 
Quote:
93 = (4!*4)  sqrt(4/.4~) 93 = 96  3 assuming .4~ is the repeating decimal that equates to .444444 OR 4/9. 

20070322, 01:06  #105 
Aug 2005
Brazil
101101010_{2} Posts 
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.

20161020, 20:36  #106 
"Robert Gerbicz"
Oct 2005
Hungary
2×3^{2}×83 Posts 
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).

20210504, 15:40  #107 
1976 Toyota Corona years forever!
"Wayne"
Nov 2006
Saskatchewan, Canada
5·953 Posts 
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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