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MatthewV
Daedalian Member :_

Posted: Wed Mar 01, 2006 11:20 pm    Post subject: 1

The objective is to is to use the randomly chosen numbers 7, 18, 5, 25, 12, 1, 2, 25,18, 9 ,14, 20, 8 to be as close to 1000pi (3141.592653...) with the smallest score. The numbers must be used in order. Mathematical symbols have the following cost:

 Code: sign  cost  example  +    free  3+9=12   -    1     5-3-1=1   (cost of 1*2=2)  *    3     4*3*3=36  (cost of 3*2=6)  /    3     20/5=4   ^    5     2^4=16    (roots can be made with ^.5 for the same cost)  ()   2     5*(2+4)=30 (NOTE: the * is not included in the cost)  !    7     4!=24      |ab|  4     |-12|=12  log   7     log100=2  (ONLY base 10) ln    7     ln60=4.094344... combining two numbers (you have 17 and 3 next to each other->173)       10 sin cos tan   100   (ONLY in radians) csc sec cot asin acos atan  1000 (arctan) (output in radians) acsc asec acot Being away from 1000pi has the cost of 5*(distance away) If you get to 3139, 5*(1000-3139)= ~12.963. This will be carried out as far as needed to break ties when possible.

 Code: Example: -7*18^.5+25*(12+1)- (log2^.25)*18*914 -20*8 = 2776.7448... 1 3  5  0  32  0  1 2 7  5    3  3 10 1  3     1824.239...  TOTAL= 1824.239+49= 1873.239

The order of operations are very important. Submissions may be PMed to me or posted in the thread.

This will end on March 14 at 11:59 Alaska Time.

Last edited by MatthewV on Thu Mar 16, 2006 8:51 am; edited 2 times in total
jeep
Daedalian Member

Posted: Thu Mar 02, 2006 12:41 am    Post subject: 2

A couple questions... what is the order of precedence used? Left to right? Root, mult/div, add/sub...??

 Code: Example: -7*18^.5+25(12+1)- (log2^.25)*18*914 -20*8 = 2776.7448... 1 3  5  0  2  0  1 2 7  5    3  3 10 1  3     1824.239...  TOTAL= 1824.239+46= 1870.239

Would 25(12+1) give you multiplication for free? I'm guessing there would need to be a * in there, right?

-JEEP
MatthewV
Daedalian Member :_

 Posted: Thu Mar 02, 2006 2:45 am    Post subject: 3 Fixed.. And jeep seems to be right. Left to right 1. powers 2. multiple/divide 3. add subtract
alphatango
Daedalian Member

 Posted: Thu Mar 02, 2006 11:22 am    Post subject: 4 Must all the given numbers be used?_________________"Hanging is too good for a man who makes puns; he should be drawn and quoted." -- Fred Allen Keeper of the Eternal Flame of the Inner Geek.
MatthewV
Daedalian Member :_

 Posted: Thu Mar 02, 2006 8:34 pm    Post subject: 5 They must all be used in order.
MatthewV
Daedalian Member :_

 Posted: Thu Mar 02, 2006 9:40 pm    Post subject: 6 For those who have tried but didn't come up with a completely awesom answer... A score of 100 is OK A score of 50 is pretty good A score is 25 or less is sweet.
Lepton*
Guest

 Posted: Sun Mar 05, 2006 12:29 am    Post subject: 7 If the inverse trig functions are allowed, then a perfect solution is possible, right? Now, to find it...
Lepton*
Guest

 Posted: Sun Mar 05, 2006 12:56 am    Post subject: 8 How about: (7 + 18) * 5 * asin( - 25 + 12 + 1 + 2 + 25 - 18 + 9 + 14 - 20) * 8 1000 * asin( 0 ) 1000 * pi Oh, I just re-read the rules. I though that the distance was multiplied by the cost, rather than added to it. I guess that gives me a cost of 1012, which sux0rs. Ah well, at least it's something to beat, right?
MatthewV
Daedalian Member :_

 Posted: Sun Mar 05, 2006 1:11 am    Post subject: 9 The distance you are away is mulitplied by 5 and then added to your score. Yup... the arc functions suck for that reason. I wanted that... And this is also because is the arcsin of 0 really equal to pi? It is also equal to 0 (a more common answer I believe).I don't mind it because it is Lepton and because all the other entries have had a lower score. Right now I have mith, Talzor, kevinatilusa, Lepton (and myself)
Lepton*
Guest

 Posted: Sun Mar 05, 2006 7:56 am    Post subject: 10 In retrospect, I just wanted to see if I could find a "perfect" solution. The arcsine functions are multi-valued, so asin(0) could equally well be 0 or 12345*pi.
mith
Pitbull of Truth

 Posted: Sun Mar 05, 2006 8:32 am    Post subject: 11 arcsin (etc.) often is defined to only give the principal values (0, for arcsin(0)). Not that it really matters here, as using the trig functions is clearly not the way to go.
/dev/joe*
Guest

 Posted: Wed Mar 08, 2006 5:23 pm    Post subject: 12 7 + (-18-5+25+12)^(1+2) + 25 + (18+9)*14 - 20 + 8 = 3142, for a score of 19 and a smidge.
Talzor
Daedalian Member

 Posted: Fri Mar 10, 2006 11:49 am    Post subject: 13 -7 - 18 + 5 + 25 - 12 - 1 + 2 * 25 * 18 + 9 + 14 * 20 * 8 for a score a smidge under 19. Sorry couldn't help myself .
Amb
Amb the Hitched.

 Posted: Sat Mar 11, 2006 7:25 am    Post subject: 14 My first attempt gives (((7*18+5)/25*12-1)*2-25-18+9)*14)*20/8) = 3141.60
Amb
Amb the Hitched.

 Posted: Sat Mar 11, 2006 7:37 am    Post subject: 15 I also have ((7 + 18) * 5 * 25 - 12) * 1 + 2 - 25 + 18 - 9 + 14 + 20 + 8 = 3141.00 which is apparently 18.9632 points?
MatthewV
Daedalian Member :_

 Posted: Sat Mar 11, 2006 7:50 am    Post subject: 16 appears the "smidge under 19" group is tied
Amb
Amb the Hitched.

 Posted: Sat Mar 11, 2006 7:58 am    Post subject: 17 Can we get an idea of what to target to steal 1st place :-p
MatthewV
Daedalian Member :_

 Posted: Sat Mar 11, 2006 8:07 am    Post subject: 18 GLAmb1089: Too lazy :-p Are you still too lazy??
Talzor
Daedalian Member

 Posted: Sat Mar 11, 2006 11:20 am    Post subject: 19 Here's something to beat amb (7 + 18) * 5 * 25 - 12 + 1 + 2 - 25 + 18 - 9 + 14 + 20 + 8 = 3142.00 = 13.0367... points
MatthewV
Daedalian Member :_

 Posted: Sat Mar 11, 2006 11:42 pm    Post subject: 20 amb and mith both found that one before you :-)
Talzor
Daedalian Member

 Posted: Sun Mar 12, 2006 1:43 am    Post subject: 21 I figure he probably had, but the on the off chance that he'd missed it I just had to post it.
MatthewV
Daedalian Member :_

 Posted: Sun Mar 12, 2006 9:02 am    Post subject: 22 You guys have a few days to break this tie for second place
Amb
Amb the Hitched.

 Posted: Sun Mar 12, 2006 6:26 pm    Post subject: 23 The numbers are code for 'Grey Labyrinth' And yes Talzor, I was going to publish that equation but MV didnt want me to. I was kinda hoping I could find Miths cheaper one but not yet. It would probably have one set of brackets, 2 multipliers and the rest add. In fact, if we knew the score of Miths, we could probably work backwards as to what has to be there. Eg if we presume 12.00 then we can probably suss out a combination that equates to roughly 3141.59 and then multiply the difference by 5? and see what we get.
mith
Pitbull of Truth

 Posted: Sun Mar 12, 2006 7:51 pm    Post subject: 24 It wasn't me that was lower. I'm lower now, though.
MatthewV
Daedalian Member :_

 Posted: Thu Mar 16, 2006 5:01 am    Post subject: 25 ooops, I will let this run 24 hours longer than it was supposed to. I doubt anyone will submit anything in the next four hours...
Amb
Amb the Hitched.

 Posted: Thu Mar 16, 2006 6:16 am    Post subject: 26 Rats - I was trying to use my programme I wrote to find answers. (The one I wrote for the worst), but it returns everything thing in the form (((x[]y)[]z)[]a) etc... Which eliminates a lot of combos where the brackets are more spread out
MatthewV
Daedalian Member :_

 Posted: Thu Mar 16, 2006 8:49 am    Post subject: 27 10 minutes early. Oh well. I included all the entries I received that were distinctly different in some manner. One of amb's in thread ones was not included...oh well... I marked the best each person sent with three stars. As noted by amb, the numbers were not random. They spell out GREYLABYRINTH. Lepton *** (7 + 18) * 5 * asin( -25 + 12 + 1 + 2 + 25 - 18 + 9 + 14 - 20) * 8 = 1000 pi Score = 1012.0000000000000000 mith (7 + 18 + 5) * (25 + 12 + 1 + 2 + 25 + 18 + 9 + 14) -20 * ln(8) = 3138.411169... Score = 33.907... mith (7 + 18 + 5 + 25) * (12 + 1 + 2 + 25 + 18) - 9 - 14 - 20 - 8 = 3139 Score = 23.963... mith (7 + 18 + 5 + 25) * (12 + 1 + 2 + 25 + 18) -log(9) +(14 - 20) * 8 = 3141.045757... Score = 23.734... mith (7 + 18 + 5 + 25) * (12 + 1 + 2 + 25 + 18) - (9 + 14 - 20)! * 8 = 3142 Score = 23.036... Talzor 7! - 18 * 5 * 25 + 12 + 1 - 2 + 25 + 18 + 9 + 14 * 20 + 8 = 3141 Score 20.963... /dev/joe*** 7 + ( -18 - 5 + 25 + 12) ^(1 + 2) + 25 + (18 + 9) * 14 - 20 + 8 = 3142 Score = 19.036... amb ((7 + 18) * 5 * 25 - 12) * 1 + 2 - 25 + 18 - 9 + 14 + 20 + 8 = 3141 Score = 18.963... Talzor -7 - 18 + 5 + 25 - 12 - 1 + 2 * 25 * 18 + 9 + 14 * 20 * 8 = 3141 Score = 18.963... kevinatilusa (7 + 18 + 5 + 25 + 12 - 1 + 2 * 25 + 18 + 9 + 14) * 20 + Ln(8) =3142.08... Score 18.433... MatthewV*** 7 + 18 + 5! * 25 + 12 + 1 + 2 * 25 + 18 + 9 + 14 + 20 - 8 = 3141 Scoring 16.963... kevinatilusa - sqrt[7] + (18 + 5 + 25 + 12 - 1 + 2 + 25 + 18 + 9 + 14 * 20) * 8 = 3141.35... Scoring 16.192... amb AND mith AND Talzor*** (7 + 18) * 5 * 25 - 12 + 1 + 2 - 25 + 18 - 9 + 14 + 20 + 8 = 3142 Scoring 13.036 mith 7 + (18 + 5 + 25) * (12 - 1 + 2 + 25 + 18 + 9) - 14 + 20 + 8 = 3141 Score = 11.963... kevinatilusa*** 7 - 18 + (5 + 25 * 12 + 1 + 2 + 25 + 18 + 9 + 14 + 20) * 8 = 3141 Scoring 11.963... mith*** - 7 + 18 - 5 + (25 + 12 + 1 + 2 + 25 + 18 + 9) * (14 + 20) + 8 = 3142 Score = 11.036732051035... Lepton gets the very large “Perfect” star /dev/joe gets a small blue star MatthewV gets a shiny purple star amb and Talzor share a lustrous bronze star kevinatilusa gets the beautiful silver star mith gets the great gold star. Thank you and congratulations to mith!
mith
Pitbull of Truth

 Posted: Thu Mar 16, 2006 5:24 pm    Post subject: 28 w00t. I put together a little spreadsheet to check for solutions of the form: numbers + (numbers added together)*(numbers added together) + numbers. I started doing it "by hand" leaving off a few numbers at the end to play with, but I eventually wrote something to check all the possible ways to split things into four groups. Also checked for possibilites using two * and one set of (), but I didn't think of trying what kevin did. After piggy-backing off amb's posted solution, I knew I couldn't use much more than that and stay lower.
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