Classic problem: Four 4's

[fetofs]

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?

[R. Gerbicz]

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 ).

[R. Gerbicz]

Part 2.:
Here is the program in four4.txt

[fetofs]

Bye bye 93!!!! I'll miss you!!!

But I can't use Gerbicz's program...
Will someone try to solve the other remaining ones?

[petrw1]

Originally Posted by fetofs

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.

[fetofs]

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.

[R. Gerbicz]

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).

[petrw1]

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.