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VoyagerKing O ho monster
Joined: 23 Aug 2006 Posts: 13 Location: Michigan

Posted: Wed Aug 23, 2006 3:13 pm Post subject: The 4 4s Puzzle 


Hello Puzzle Community!
I would like to post a puzzle for you, and see how well you do with it. I'd like you to work together on it, as I will keep track of your answers through your collective posts.
There is a time limit. You'll have from now until sometime on Friday to complete this little puppy.
I call the puzzle The 4 4s.
All you have to do is combine 4 4s, along with any legitimate mathematical symbols, to produce 60 expressions representing the integers from 1 to 60.
Here is an example:
16 = 4 + 4 + 4 + 4
Using 4 4s, and the math symbol the plus sign, I have produced an expression for the integer 16.
There! 1 down, just 59 to go!
GOOD LUCK!
VoyagerKing _________________ VoyagerKing 

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Titanium22 your chamber lye breeds fleas
Joined: 14 Sep 2003 Posts: 12253

Posted: Wed Aug 23, 2006 3:22 pm Post subject: 


Is this the sort of thing you mean...?
60 = [(4x4) x 4]  4
T22 _________________ Puzzletome  for serious riddlers 

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VoyagerKing O ho monster
Joined: 23 Aug 2006 Posts: 13 Location: Michigan

Posted: Wed Aug 23, 2006 3:28 pm Post subject: 


T22,
You recently posted:
60 = [(4x4) x 4]  4
YES, that is Exactly the sort of thing I'm looking for!
Updated Solving List:
16 = 4 + 4 + 4 + 4
60 = [(4x4) x 4]  4
2 down, just 58 to go! _________________ VoyagerKing 

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aki Four of thy five wits went halting off
Joined: 06 Mar 2004 Posts: 3274

Posted: Wed Aug 23, 2006 4:14 pm Post subject: 


60 = (4x4x4)  4
59 = 4!/.4  4/4
58 = 4!/.4  4/sqrt(4)
57 = (4!sqrt(4))/.4 + sqrt(4)
56 = 4! + 4! + 4 + 4
55 = (4!4+sqrt(4))/.4
54 = (4!4)/.4 + 4
53 = (4!sqrt(4))/.4  sqrt(4)
52 = 4! + 4! + sqrt(4) + sqrt(4)
51 = (4!sqrt(4))/.4  4
Last edited by aki on Wed Aug 23, 2006 6:39 pm; edited 2 times in total 

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gordel Banbury cheese
Joined: 24 Jul 2004 Posts: 150

Posted: Wed Aug 23, 2006 4:18 pm Post subject: 


(4+4)/(4+4) = 1
(4/4)+(4/4) = 2
(4+4+4)/4 = 3
(4/4)+[4(4/4)] = 4
Hope I am doing it right. 

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4x4 You, minion, are too saucy
Joined: 12 Feb 2004 Posts: 927 Location: Belgium

Posted: Wed Aug 23, 2006 4:21 pm Post subject: 


gordel wrote: 
(4/4)+[4(4/4)] = 4
Hope I am doing it right. 
I'm afraid you have 5 4's here
1 = 4  4 + (4/4)
2 = (4/4) + (4/4)
3 = (4 + 4 + 4) / 4
4 = [4/.4  sqrt(4)] / sqrt(4)
5 = (4x4 + 4) / 4
6 = (4! / 4) + 4  4
7 = (4+4)  (4/4)
8 = 4 + 4 + 4  4
9 = 4/.4  4/4
10 = 4/.4 + 4  4
Last edited by 4x4 on Wed Aug 23, 2006 4:33 pm; edited 3 times in total 

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gordel Banbury cheese
Joined: 24 Jul 2004 Posts: 150

Posted: Wed Aug 23, 2006 4:23 pm Post subject: 


I never could count Try again.
sqrt(4*4)*(4/4) = 4 

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4x4 You, minion, are too saucy
Joined: 12 Feb 2004 Posts: 927 Location: Belgium

Posted: Wed Aug 23, 2006 4:32 pm Post subject: 


much better 

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xyphic Forum git
Joined: 14 Sep 2003 Posts: 2797 Location: Cambridge, UK

Posted: Wed Aug 23, 2006 4:35 pm Post subject: 


4 = 4 + 4  sqrt(4)  sqrt(4)
11 = (4! / sqrt(4))  (4 / 4)
12 = (4 x 4)  sqrt(4)  sqrt(4)
13 = (4! / sqrt(4)) + (4 / 4)
14 = (4 x 4)  4 + sqrt(4)
15 = (4 x 4)  (4 / 4)
16 = sqrt(4) x sqrt(4) x sqrt(4) x sqrt(4)
17 = (4 x 4) + (4 / 4)
18 = (4! / sqrt(4)) + 4 + sqrt(4)
19 = 4!  4  (4 / 4)
20 = ((4! x 4) / 4)  4 _________________ Puzzletome  Confusion now hath made his masterpiece! 

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xyphic Forum git
Joined: 14 Sep 2003 Posts: 2797 Location: Cambridge, UK

Posted: Wed Aug 23, 2006 4:40 pm Post subject: 


21 = 4!  4 + (4 / 4)
22 = (4 x 4) + 4 + sqrt(4)
23 = 4!  ((4 / 4) ^ 4)
24 = 4!  4 + sqrt(4) + sqrt(4)
25 = 4! + ((4 / 4) ^ 4) _________________ Puzzletome  Confusion now hath made his masterpiece! 

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carolanne Pestilent congregation of vapours
Joined: 16 Mar 2005 Posts: 657 Location: Morse Country

Posted: Wed Aug 23, 2006 4:48 pm Post subject: 


Is this right?
26 = 4! + sqrt(4) + 4  4
(had to ask what 4! means) 

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carolanne Pestilent congregation of vapours
Joined: 16 Mar 2005 Posts: 657 Location: Morse Country

Posted: Wed Aug 23, 2006 4:56 pm Post subject: 


26 = 4! + sqrt(4) + 4  4
27 = 4! + sqrt(4) + (4 / 4)
28 = 4! + 4 + 4  4
29 = 4! + 4 + (4 / 4)
30 = 4! + 4 + sqrt(4)
Hope I'm doing this right. If not, can someone tell me what I'm doing wrong.
CA 

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VoyagerKing O ho monster
Joined: 23 Aug 2006 Posts: 13 Location: Michigan

Posted: Wed Aug 23, 2006 6:02 pm Post subject: Updated Solving List #2 


Man,
Go away for a little lunch, and you guys post a bunch!
Ok, I'm going to digest so many of your posts, and do an update, then, review the rest, and do one more.
First off, the expression posted for 58 was incorrect. Please correct and try again. What was posted was:
58 = 4!/.4 + 4/sqrt(4)
Also, the post for 55 had a typo:
55 = (4!4+rt(4))/.4
I believe the author meant to say:
55 = (4!4+sqrt(4))/.4
Finally, the expression for 4 had 5 4s:
(4/4)+[4(4/4)] = 4
But, the author reposted with:
sqrt(4*4)*(4/4) = 4
Cool!
Here is my first of 2 new Updated Solving Lists:
1 = (4+4)/(4+4)
2 = (4/4)+(4/4)
3 = (4+4+4)/4
4 = sqrt(4*4)*(4/4)
5 = (4x4 + 4) / 4
6 = (4! / 4) + 4  4
7 = (4+4)  (4/4)
8 = 4 + 4 + 4  4
9 = 4/.4  4/4
10 = 4/.4 + 4 – 4
16 = 4 + 4 + 4 + 4
51 = (4!sqrt(4))/.4 – 4
52 = 4! + 4! + sqrt(4) + sqrt(4)
53 = (4!sqrt(4))/.4  sqrt(4)
54 = (4!4)/.4 + 4
56 = 4! + 4! + 4 + 4
57 = (4!sqrt(4))/.4 + sqrt(4)
59 = 4!/.4  4/4
60 = [(4x4) x 4] – 4
Whew! Now hang on! Let me see what else you have posted, and I will soon post another Updated Solving List. _________________ VoyagerKing 

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Robin Scurvy, old, filthy, scurry lord
Joined: 06 Mar 2004 Posts: 501 Location: Durham, England

Posted: Wed Aug 23, 2006 6:13 pm Post subject: 


The 58 example is easily corrected:
58=4!/.4  4/SQRT(4)
(although I think the use of the factorial sign, not to mention the decimal point, is distinctly dodgy ) 

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VoyagerKing O ho monster
Joined: 23 Aug 2006 Posts: 13 Location: Michigan

Posted: Wed Aug 23, 2006 6:21 pm Post subject: Updated Solving List #3 


Ok! First the bad news:
The expression posted for 30:
30 = 4! + 4 + sqrt(4)
only has 3 4s. Please correct and try again.
Other than that, everything else was cool!
Here is the latest Updated Solving List:
1 = (4+4)/(4+4)
2 = (4/4)+(4/4)
3 = (4+4+4)/4
4 = sqrt(4*4)*(4/4)
5 = (4x4 + 4) / 4
6 = (4! / 4) + 4  4
7 = (4+4)  (4/4)
8 = 4 + 4 + 4  4
9 = 4/.4  4/4
10 = 4/.4 + 4 – 4
11 = (4! / sqrt(4))  (4 / 4)
12 = (4 x 4)  sqrt(4)  sqrt(4)
13 = (4! / sqrt(4)) + (4 / 4)
14 = (4 x 4)  4 + sqrt(4)
15 = (4 x 4)  (4 / 4)
16 = 4 + 4 + 4 + 4
17 = (4 x 4) + (4 / 4)
18 = (4! / sqrt(4)) + 4 + sqrt(4)
19 = 4!  4  (4 / 4)
20 = ((4! x 4) / 4) – 4
21 = 4!  4 + (4 / 4)
22 = (4 x 4) + 4 + sqrt(4)
23 = 4!  ((4 / 4) ^ 4)
24 = 4!  4 + sqrt(4) + sqrt(4)
25 = 4! + ((4 / 4) ^ 4)
26 = 4! + sqrt(4) + 4 – 4
27 = 4! + sqrt(4) + (4 / 4)
28 = 4! + 4 + 4  4
29 = 4! + 4 + (4 / 4)
51 = (4!sqrt(4))/.4 – 4
52 = 4! + 4! + sqrt(4) + sqrt(4)
53 = (4!sqrt(4))/.4  sqrt(4)
54 = (4!4)/.4 + 4
56 = 4! + 4! + 4 + 4
57 = (4!sqrt(4))/.4 + sqrt(4)
59 = 4!/.4  4/4
60 = [(4x4) x 4] – 4
You guys are doing Great!
37 down, just 23 to go! _________________ VoyagerKing 

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