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Posted: 8/23/2005 1:50 PM
Post subject: The Four Fours challenge (math)
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nesrocks
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Player (247)
Joined: 5/1/2004
Posts: 4096
Location: Rio, Brazil
The challenge is to write sentences which result in integer numbers from 0 to 100 using only four "4". Any math symbol is accepted, even those which have implicit "2" like square root, as long as you don't write any other algarism, you can use any symbol. Example: 0 = 44 - 44 1 = 4/4 + 4 - 4 2 = 4 + 4 - 4 - √4 (square root) 3 = ... and so on You must use ALL four fours on every sentence. Sentences with more or less than four fours aren't valid. You can't use letters like "lim" or "log" Usefull hints: you can write "44" (uses 2 of the four fours) and "444" etc. use ! example: 4! = 4 x 3 x 2 x 1 = 24 use ? (limiar factor) example: 4? = 4 + 3 + 2 + 1 = 10 use exponential represented by ^ example: 4^4 = 256 use square root at will represent by "√" example: √4 = 2 of course, use (), [] and {} at will i won't give any other hints ;) btw, the problem is 100% solvable! all 101 numbers can be written that way. hf PS.: don't go looking on the internets for answers!
aka Nesrocks http://www.youtube.com/user/UoBtExFODA https://nesrocks.com https://twitter.com/bitinkstudios
Posted: 8/23/2005 2:16 PM
(Edited: 8/23/2005 2:31 PM)
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Xaphan
Former player
Joined: 5/24/2005
Posts: 405
Location: France
I got 3 = ( 4 ? + 4 - √ 4 ) / 4 4 = √ 4 + √ 4 + √ 4 - √ 4 5 = ( 4 x 4 + 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 ? + [ ( √ 4 + √ 4 ) / 4 ] 12 = [ ( 4 ? + √ 4 ) / 4 ] * 4 13 = 4 ? + [ ( 4 ? + √ 4 ) / 4 ] 14 = 4 ? + 4 + 4 - 4 15 = 4 ? + 4 + 4 / 4 16 = 4 ? + √ 4 + √ 4 + √ 4 17 = 4 ! - [ ( 4 ? + 4 ) / √ 4 ] 18 = 4 ? + 4 + √ 4 + √ 4 19 = ( 4 ? - 4 / 4 ) + 4 ? 20 = 4 x 4 + √ 4 + √ 4 I will stop here for now... Tell me if some are wrong or if i was bypassing the rules (i hop that you can use the √ twice in the same line...)
Not dead yet... still very busy... damn...
Posted: 8/23/2005 2:22 PM
(Edited: 8/23/2005 2:33 PM)
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nesrocks
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Player (247)
Joined: 5/1/2004
Posts: 4096
Location: Rio, Brazil
always use spacing between symbols please, "-" before the "√" is barelly seable :) i think you meant 17 = 4 ! + [ ( 4 ? + 4 ) / √ 4 ] 80 to go :)
aka Nesrocks http://www.youtube.com/user/UoBtExFODA https://nesrocks.com https://twitter.com/bitinkstudios
Posted: 8/23/2005 2:23 PM
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Walker_Boh
Former player
Joined: 4/16/2004
Posts: 1276
Location: Uppsala, Sweden
What's the ?-mark? I know the ! (4! = 4 x 3 x 2 x 1= 24) but the ?-mark I don't know. Nice though ;)
/Walker Boh
Posted: 8/23/2005 2:33 PM
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Xaphan
Former player
Joined: 5/24/2005
Posts: 405
Location: France
4? is the summing operator, it works like the ! operator though you have to add the number between them instead of multiplying them... I shall try to find the others tonight... that's a nice guess FODA
Not dead yet... still very busy... damn...
Posted: 8/23/2005 2:35 PM
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nesrocks
He/Him
Player (247)
Joined: 5/1/2004
Posts: 4096
Location: Rio, Brazil
another issue is to find out how far can one go beyond 100 without breaking the rules ;)
aka Nesrocks http://www.youtube.com/user/UoBtExFODA https://nesrocks.com https://twitter.com/bitinkstudios
Posted: 8/23/2005 2:39 PM
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NrgSpoon
Joined: 6/14/2004
Posts: 646
Xaphan: 16 = 4 ? + √ 4 + √ 4 + √ 4 Kinda overcomplicated here. 4+4+4+4 not good enough?
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Posted: 8/23/2005 3:24 PM
(Edited: 8/23/2005 3:34 PM)
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Itstoearly
Joined: 8/10/2004
Posts: 173
Location: Bethel, VT
16 also = 4 * 4 * 4 / 4 --------------------------- 21 = (44 - √4) / ( √4) 22 = 4 * 4 + 4 + √4 23 = (44 + √4) / ( √4) 24 = 4 * 4 + 4 + 4 25 = 4? * √4 + [(4?) / ( √4)] 26 = 4! + 4 - 4 + √4 27 = 4! + (4/4) + √4 28 = 4! + 4 - 4 + 4 29 = 4! + (4/4) + 4 30 = 4 * 4 * √4 - √4
Posted: 8/23/2005 3:34 PM
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Xaphan
Former player
Joined: 5/24/2005
Posts: 405
Location: France
And so...? easiness is not my moto ;) I shall go for some more : 21 = 4 ? + 4 ? + 4 / 4 22 = 4 ! - √ 4 + √ 4 - √ 4 23 = 4 ! - √ 4 + 4 / 4 24 = ( 4 ? + 4 - √ 4 ) x √ 4 25 = 4 ! + √ 4 - 4 / 4 26 = 4 ! + √ 4 + √ 4 - √ 4 27 = 4 ! + ( 4 ? + √ 4 ) / 4 28 = 4 ! + 4 + 4 - 4 29 = ( 4 ! + 4 ! + 4 ? ) / √ 4 30 = 4 ! + √ 4 + √ 4 + √ 4 I shall post them ten by ten it shall be easier to read
Not dead yet... still very busy... damn...
Posted: 8/23/2005 3:37 PM
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Itstoearly
Joined: 8/10/2004
Posts: 173
Location: Bethel, VT
31 = 4! + 4? - 4/4 32 = 4 * 4 + 4 * 4
Posted: 8/23/2005 4:12 PM
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Xaphan
Former player
Joined: 5/24/2005
Posts: 405
Location: France
33 = 4 ? + 4 ! - 4 / 4 34 = 4 x 4 x √ 4 + √ 4 35 = 4 ? + 4 ! + 4 / 4 36 = 44 - 4 x √ 4 37 = ????????????????????? 38 = 4 ! + 4 ? + √ 4 + √ 4 39 = 4 x 4 ? - 4 / 4 40 = 4 x 4 ? + 4 - 4 41 = 4 x 4 ? + 4 / 4 42 = 4 x 4 ? + 4 - √ 4 43 = ( 4 ! x 4 - 4 ? ) / √ 4
Not dead yet... still very busy... damn...
Posted: 8/23/2005 5:26 PM
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SXL
Joined: 2/7/2005
Posts: 571
Xaphan wrote:
33 = 4 ? + 4 ! - 4 / 4
Itstoearly wrote:
31 = 4! + 4? - 4/4
first is correct, but 31 is wrong... please redo every line before posting it :)
I never sleep, 'cause sleep is the cousin of death - NAS
Posted: 8/23/2005 7:37 PM
(Edited: 8/23/2005 7:41 PM)
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Randil
Skilled player (1828)
Joined: 4/20/2005
Posts: 2161
Location: Norrköping, Sweden
Well, this seems like a lot of fun... I think I'll try to solve this tomorrow if I get the time... Oh and here's 37: 37 = (4+4)? + (4/4) I don't know how to write the square-root symbol, so I'll write sqrt instead. here's the solution to 31: (sqrt4+sqrt4+sqrt4)? + 4?
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Posted: 8/23/2005 7:37 PM
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samurai_goroh
Editor, Player (54)
Joined: 12/25/2004
Posts: 634
Location: Aguascalientes, Mexico
44 = 44 x (4 / 4) 45 = 44 + (4 / 4) 46 = 44 + (4 / √4) 47 = 48= (4? * 4) + 4 + 4
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Posted: 8/23/2005 7:47 PM
(Edited: 8/23/2005 7:58 PM)
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Randil
Skilled player (1828)
Joined: 4/20/2005
Posts: 2161
Location: Norrköping, Sweden
47 = 4! + 4! - (4/4) 49 = 4! + 4! + (4/4) 50 = 4! + 4! + (4/sqrt4) 51 = (4+4+sqrt4)? + 4 52 = (4?)? - sqrt4 + (4/4) (this one was a little tricky) 53 = (4?)? - (4+4)/4
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Posted: 8/23/2005 7:55 PM
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Quietust
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Emulator Coder, Former player
Joined: 7/14/2004
Posts: 250
52 = 4! + 4! + √4 + √4
* Quietust, QMT Productions P.S. If you don't get this note, let me know and I'll write you another
Posted: 8/23/2005 7:59 PM
(Edited: 8/23/2005 8:01 PM)
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Randil
Skilled player (1828)
Joined: 4/20/2005
Posts: 2161
Location: Norrköping, Sweden
hehe I guess your answer to 52 is simpler than mine Quietust :) 54 = (4?)? -((sqrt4+sqrt4)/4)
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Posted: 8/23/2005 8:00 PM
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Quietust
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Joined: 7/14/2004
Posts: 250
Also, 51 = (4 + 4 + √4)? - 4, not + 4
* Quietust, QMT Productions P.S. If you don't get this note, let me know and I'll write you another
Posted: 8/23/2005 8:02 PM
(Edited: 8/23/2005 8:12 PM)
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Randil
Skilled player (1828)
Joined: 4/20/2005
Posts: 2161
Location: Norrköping, Sweden
Ah, yes you're right. I hate it when I do stuff like that. 55 = (4?)? + (4-4)/4 56 = (4?)? + (sqrt4+sqrt4)/4 57 = (4?)? + (4+4)/4 58 = (4?)? + (4?+sqrt4)/4 59 = (4+4+sqrt4)? + 4 60 = 4! + 4! + 4? + sqrt4 61 = (4?)? + sqrt4 + sqrt4 + sqrt4 62 = (4?+sqrt4)? - 4*4 63 = (4?)? + 4 + sqrt4 + sqrt4
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Posted: 8/23/2005 8:12 PM
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Vatchern
Player (86)
Joined: 3/8/2005
Posts: 973
Location: Newfoundland, Canada
62 = 4! + 4! + 4! - 4? i think
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Posted: 8/23/2005 8:14 PM
(Edited: 8/23/2005 8:18 PM)
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Randil
Skilled player (1828)
Joined: 4/20/2005
Posts: 2161
Location: Norrköping, Sweden
Vatchern wrote:
62 = 4! + 4! + 4! - 4? i think
Yes that is correct, 4! + 4! + 4! - 4? = 24*3 - 10 = 72-10= 62 64 = (sqrt4+sqrt4)*4*4 65 = (4?)? + 4? +4 -4 66 = (4?)? +4? + (4/4)
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Posted: 8/23/2005 8:16 PM
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Vatchern
Player (86)
Joined: 3/8/2005
Posts: 973
Location: Newfoundland, Canada
64 is also 4root4 x 4root4
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Posted: 8/23/2005 8:18 PM
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Walker_Boh
Former player
Joined: 4/16/2004
Posts: 1276
Location: Uppsala, Sweden
Vatchern wrote:
62 = 4! + 4! + 4! - 4? i think
Isn't that 68? 24+24+24-4 = 68
/Walker Boh
Posted: 8/23/2005 8:18 PM
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Vatchern
Player (86)
Joined: 3/8/2005
Posts: 973
Location: Newfoundland, Canada
68 = 4! + 4! + 4! - 4
http://tasvideos.org/Vatchern.html
Posted: 8/23/2005 8:19 PM
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Vatchern
Player (86)
Joined: 3/8/2005
Posts: 973
Location: Newfoundland, Canada
4? = 10
http://tasvideos.org/Vatchern.html
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