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VoyagerKing
O ho monster


Joined: 23 Aug 2006
Posts: 13
Location: Michigan

PostPosted: Wed Aug 23, 2006 3:13 pm    Post subject: The 4 4s Puzzle Reply with quote

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
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Titanium22
your chamber lye breeds fleas


Joined: 14 Sep 2003
Posts: 12253

PostPosted: Wed Aug 23, 2006 3:22 pm    Post subject: Reply with quote

Is this the sort of thing you mean...?

60 = [(4x4) x 4] - 4


T22
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VoyagerKing
O ho monster


Joined: 23 Aug 2006
Posts: 13
Location: Michigan

PostPosted: Wed Aug 23, 2006 3:28 pm    Post subject: Reply with quote

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!
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aki
The portrait of a blinking idiot


Joined: 06 Mar 2004
Posts: 3025

PostPosted: Wed Aug 23, 2006 4:14 pm    Post subject: Reply with quote

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

PostPosted: Wed Aug 23, 2006 4:18 pm    Post subject: Reply with quote

(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

PostPosted: Wed Aug 23, 2006 4:21 pm    Post subject: Reply with quote

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

PostPosted: Wed Aug 23, 2006 4:23 pm    Post subject: Reply with quote

I never could count Very Happy 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

PostPosted: Wed Aug 23, 2006 4:32 pm    Post subject: Reply with quote

much better Thumbs up Very Happy
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xyphic
Forum git


Joined: 14 Sep 2003
Posts: 2692
Location: Cambridge, UK

PostPosted: Wed Aug 23, 2006 4:35 pm    Post subject: Reply with quote

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
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xyphic
Forum git


Joined: 14 Sep 2003
Posts: 2692
Location: Cambridge, UK

PostPosted: Wed Aug 23, 2006 4:40 pm    Post subject: Reply with quote

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)
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carolanne
Pestilent congregation of vapours


Joined: 16 Mar 2005
Posts: 657
Location: Morse Country

PostPosted: Wed Aug 23, 2006 4:48 pm    Post subject: Reply with quote

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

PostPosted: Wed Aug 23, 2006 4:56 pm    Post subject: Reply with quote

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

PostPosted: Wed Aug 23, 2006 6:02 pm    Post subject: Updated Solving List #2 Reply with quote

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.
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Robin
Scurvy, old, filthy, scurry lord


Joined: 06 Mar 2004
Posts: 501
Location: Durham, England

PostPosted: Wed Aug 23, 2006 6:13 pm    Post subject: Reply with quote

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 Razz )
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VoyagerKing
O ho monster


Joined: 23 Aug 2006
Posts: 13
Location: Michigan

PostPosted: Wed Aug 23, 2006 6:21 pm    Post subject: Updated Solving List #3 Reply with quote

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!
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