07-26-2007, 12:15 PM | #1 |
FFR Player
Join Date: Jul 2007
Posts: 8
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4 4's puzzle
Alright, so here's how the game is played:
You're trying to make as many numbers as possible using 4 4's or less, in an attempt to try to prove an old theory: "You can make any whole number using only four instances of the number four and commonly used mathematical symbols." So so far, the symbols allowed are: 1. All standard mathematical operators (+-*/) 2. Factorials (n! = n * (n-1) * (n-2) * ... * 2 * 1) 3. Square roots, arbitrary roots (the index is included in the 4 4's) 4. Repeat signs (denoted with an apostrophe ' or grave accent `, ex. 0.3` = 0.33333.....) 5. Exponentiation (denoted with a caret ^, 2^8 = 2*2*2*2*2*2*2*2, 8 2's) 6. Decimals do not require a leading zero. So you could put .4 instead of 0.4. I'll start: 0 = 4-4 1 = 4/4 2 = sqrt(4) 3 = 4 - 4/4 4 = 4 5 = 4 + 4/4 6 = 4 + sqrt(4) 7 = 4 + 4 - 4/4 8 = 4 + 4 9 = 4 + 4 + 4/4 10 = 4 + 4 + sqrt(4) And the next person would continue from 11, 12, and so on, and introduce new symbols and explaining them if necessary. |
07-26-2007, 02:40 PM | #2 |
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Re: 4 4's puzzle
Stuck on 11 eh? Fail.
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07-27-2007, 04:42 PM | #3 |
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Join Date: Jul 2007
Posts: 8
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Re: 4 4's puzzle
No I'm not stuck on 11. I just want the next person to continue.
11 = 44/4 12 = (44 + 4) / 4 13 = 44/4 + sqrt(4) 14 = (4!) / sqrt(4) + sqrt(4) 15 = 44/4 + 4 16 = 4 * 4 17 = 4 * 4 + 4/4 18 = 4 * 4 + sqrt(4) 19 = 4! - 4 - 4/4 20 = 4! - 4 And so on... |
07-27-2007, 04:55 PM | #4 |
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Location: Manchester, England
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Re: 4 4's puzzle
I remember doing this as a personal project in high school, except that I used exactly 4 4s for each number. As far as I can recall, 113 is the smallest number that can't be done using those rules. Anyway, it goes something like...
21 = 4! - 4 + 4/4 22 = 4! - sqrt(4) (*4/4) 23 = 4! + 4/4 - sqrt(4) 24 = 4! = (4 + 4 + 4) * sqrt(4) 25 = 4! + 4/4 = 4! + sqrt(4) - 4/4 etc. |
07-27-2007, 05:02 PM | #5 |
Digital Dancing!
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Re: 4 4's puzzle
28= 4!(4/4)-4
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07-28-2007, 04:26 PM | #6 |
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Re: 4 4's puzzle
29 = 4! + 4 + 4/4
30 = 4! + 4 + sqrt(4) 31 = 4! + 4/.4' - sqrt(4) 32 = 4 * 4 + 4 * 4 33 = 4! - 4/.4' 34 = 4! + 4 + 4 + sqrt(4) |
07-29-2007, 04:03 AM | #7 |
I only need 3 seconds :)
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Re: 4 4's puzzle
35 = 4! + 44/4
36 = 4 + 4 + 4 + 4! 37 = 4! + (4! + sqrt(4))/ (sqrt(4)) 38 = 4! + 4! + 4/.4 39 = 4! + 4!/(4*.4) 40 = 44 - sqrt(4) - sqrt(4) 41 = (4! + sqrt(4))/.4 - 4! 42 = 44-4+sqrt(4) 43 = 44 - 4/4 44 = 44 - 4 + 4 45 = 44 + 4/4 46 = 44 + 4 - sqrt(4) 47 = 4! + 4! - 4/4 48 = 4! + 4! + 4 - 4 |
07-29-2007, 06:57 AM | #8 |
Private College
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Re: 4 4's puzzle
I was going to write an exciting proof, but then I realized that (4!!!!!!!!!)! + 4!!!!!!!!! + 3 is impossible to get anyways.
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09-26-2007, 12:44 AM | #9 |
Banned
Join Date: Sep 2007
Posts: 20
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Re: 4 4's puzzle
49 = 4! + 4! + 4/4
50 = 4! + 4! + sqrt(4) |
09-27-2007, 04:51 PM | #10 |
FFR Veteran
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Re: 4 4's puzzle
.rouge don't bump old topics.
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09-28-2007, 12:57 AM | #11 |
Falcon Paaaauuuunch!!!!!!
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Re: 4 4's puzzle
That is possible. You just have to use (4!!!!!!!!!)! + 4!!!!!!!!! + 4 - the infinitieth root of 4 lolz.
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10-3-2007, 06:45 PM | #12 |
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Re: 4 4's puzzle
51= (4! - 4 + .4)/.4
52= sqrt(4)(4!) + 4
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10-6-2007, 05:59 PM | #13 |
Falcon Paaaauuuunch!!!!!!
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Re: 4 4's puzzle
53= (4! - sqrt(4))/.4 - sqrt(4)
54= 4!/.4 - 4 - sqrt(4) 55= (4! - sqrt(4))/.4 56= 4!/.4 - 4 57= (4! - sqrt(4))/.4 +sqrt(4) 58= 4!/.4 - sqrt(4) 59= 4!/.4 - 4/4 60= 4!/.4 61= 4!/.4 + 4/4 62= 4!/.4 + sqrt(4) 63= (4! + sqrt(4))/.4 - sqrt(4) 64= 4!/.4 + 4 65= (4! + sqrt(4))/.4 66= 4!/.4 + sqrt(4) + 4 67= (4! + sqrt(4))/.4 + sqrt(4) 68= 4!/.4 + 4 + 4 69= (4! + sqrt(4))/.4 + 4 70= (4! +4)/.4
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