20110216, 19:37  #1 
Jun 2009
676_{10} Posts 
Some fourplay
Hi folks,
I've been trying to follow the rules of a little game I found in a footnote in Reader's Digest (no joke) and it turned out to be more fun than I expected. But now I'm stuck. Here are the rules: Try to calculate the number 1, 2, 3, 4, ..... by using EXACTLY four instances of the number "four" and any combination of the following operations: + addition  subtraction * multiplacation / division ^ exponentiation SQRT square root ! faculty some examples: 1 = (4+4)/(4+4) 10 = 4*4  4!/4 20 = 4*(4!/4)  4 Getting 1 to 10 is a matter of minutes, 11 to 20 takes substantially longer, then it gets difficult, especially for odd numbers. I tried this with fellow students, later with colleagues and we took this quite a distance. But there are still two gaps on the way to 50 (those being 39 and 43). How far can you take it? Have fun! (and help me fill the last gaps please...) Peter Last fiddled with by PuzzlePeter on 20110216 at 19:38 
20110216, 19:51  #2 
"Ben"
Feb 2007
2^{3}×419 Posts 
Slightly different rules, maybe, but see:
http://www.mersenneforum.org/showthread.php?t=4756 and http://www.mersenneforum.org/showthread.php?t=7051 
20110216, 20:04  #3  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
2×3×1,733 Posts 
Quote:
Note that if the log() function is allowed it is quite easy to produce all integers from four fours. Paul Last fiddled with by xilman on 20110216 at 20:05 Reason: Fix tyypo 

20110216, 21:11  #4  
"Forget I exist"
Jul 2009
Dumbassville
2^{6}·131 Posts 
Quote:
number freak 1 to 200 pg. 187 has the answer to how far using simple expressions. 

20110216, 22:18  #5 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
3×3,061 Posts 
Re: Some fourplay
The natural thing to follow fourplay is six.

20110216, 22:27  #6 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
5889_{10} Posts 

20110216, 23:13  #7 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
3×3,061 Posts 
I am not going three elabornine...

20110217, 14:20  #8 
Mar 2007
Austria
456_{8} Posts 
Solved it (without computer help) upto n=33.
I'm surprised you found a solution for it as I think it's not possible with the current allowed ops. 
20110217, 17:06  #9  
Jun 2009
2^{2}·13^{2} Posts 
Quote:
Quote:
33 = (SQRT(SQRT(SQRT(4^4!)))+SQRT(4))/(SQRT(4)) 

20110217, 18:00  #10 
Mar 2007
Austria
2×151 Posts 
thx
had not used exponentation in my calculations. lets see if I cand find something for n=39 
20110217, 18:15  #11 
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
2×3×1,733 Posts 
An oldie, but I maintain the old ones are the best:
Q: what comes between fear and sex? A: fΓΌnf I love bilingual wordplay (but bilingual fourplay I'll leave to your imagination). Ask me sometime about trilingual puns... Paul Last fiddled with by xilman on 20110217 at 18:16 Reason: Add missing ltter in a typo 
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