mersenneforum.org Some four-play
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 2011-02-16, 19:37 #1 Puzzle-Peter     Jun 2009 66910 Posts Some four-play 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 Puzzle-Peter on 2011-02-16 at 19:38
 2011-02-16, 19:51 #2 bsquared     "Ben" Feb 2007 1100101011102 Posts Slightly different rules, maybe, but see: http://www.mersenneforum.org/showthread.php?t=4756 and http://www.mersenneforum.org/showthread.php?t=7051
2011-02-16, 20:04   #3
xilman
Bamboozled!

May 2003
Down not across

22·41·61 Posts

Quote:
 Originally Posted by Puzzle-Peter 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
Oh no, not again. This really is a mouldy oldie.

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 2011-02-16 at 20:05 Reason: Fix tyypo

2011-02-16, 21:11   #4
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

26×131 Posts

Quote:
 Originally Posted by Puzzle-Peter 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

number freak 1 to 200 pg. 187 has the answer to how far using simple expressions.

 2011-02-16, 22:18 #5 Batalov     "Serge" Mar 2008 Phi(3,3^1118781+1)/3 2×3×5×7×43 Posts Re: Some four-play The natural thing to follow four-play is six.
2011-02-16, 22:27   #6
retina
Undefined

"The unspeakable one"
Jun 2006
My evil lair

22×29×47 Posts

Quote:
 Originally Posted by Batalov The natural thing to follow four-play is six.
Going fourth and multiplying?

 2011-02-16, 23:13 #7 Batalov     "Serge" Mar 2008 Phi(3,3^1118781+1)/3 234616 Posts I am not going three elabornine...
 2011-02-17, 14:20 #8 nuggetprime     Mar 2007 Austria 30210 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.
2011-02-17, 17:06   #9
Puzzle-Peter

Jun 2009

3×223 Posts

Quote:
 Originally Posted by xilman Note that if the log() function is allowed it is quite easy to produce all integers from four fours.
Well, the rules are a bit more difficult (no square, no decimal point, no concatenation) than in the posts I was pointed at (thanks for looking them up, bsquared!) and I can't find the last missing solutions. If you can do them, please do so!

Quote:
 Originally Posted by nuggetprime 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.
Not a computer, but a calculator helped find this:

33 = (SQRT(SQRT(SQRT(4^4!)))+SQRT(4))/(SQRT(4))

 2011-02-17, 18:00 #10 nuggetprime     Mar 2007 Austria 12E16 Posts thx had not used exponentation in my calculations. lets see if I cand find something for n=39
2011-02-17, 18:15   #11
xilman
Bamboozled!

May 2003
Down not across

22·41·61 Posts

Quote:
 Originally Posted by Batalov The natural thing to follow four-play is six.
An oldie, but I maintain the old ones are the best:

Q: what comes between fear and sex?

A: fünf

I love bilingual wordplay (but bilingual four-play I'll leave to your imagination). Ask me sometime about trilingual puns...

Paul

Last fiddled with by xilman on 2011-02-17 at 18:16 Reason: Add missing ltter in a typo

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