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dimis
Responsible
Supreme Hero
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posted March 04, 2008 05:09 PM |
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Edited by dimis at 18:43, 04 Mar 2008.
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Nice Binabik. 
Now, find the shortest one! 
The one you uploaded is not the shortest.
@ Fog: Perhaps you could successively square it, so that you can get rid of the square roots. In the end you'll have a 4 degree polynomial which (with luck) you will be able to solve it. I'll check it out soon and let you know.
You 've got the idea, but I am not sure you 'll find all the minimum solutions.
edit: Now that I think about it again, you are probably right and you have all solutions with some justification.
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dimis
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posted March 05, 2008 12:04 AM |
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Edited by dimis at 00:17, 05 Mar 2008.
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FOG function
Here is your function FriendOfGunnar:
Now how would you achieve minimum without actually solving the equation?
edit: Still!!! Even if you find the minimum in your case, there is a shorter route! So, you have to find the minimum among a family of functions, and then take the minimum once again. Or, ... try another approach?
In particular, can you find a route with length exactly 40? (<-- you can do better than this as well). I loved this problem!
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friendofgunnar
Honorable
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able to speed up time
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posted March 05, 2008 12:55 AM |
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Quote:
Even if you find the minimum in your case, there is a shorter route!
brb
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Binabik
Responsible
Legendary Hero
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posted March 05, 2008 01:09 AM |
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brb
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friendofgunnar
Honorable
Legendary Hero
able to speed up time
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posted March 05, 2008 01:20 AM |
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okay, this must be it:
Find all W for which
((6+12+w)^2 + 31^2)^.5 + ((6-w)^2 + 1)^.5 < 42
at W = 6 the total length is 40.2
at W = 0 the total length is 41.92
maybe the answer dips below 40 somewhere in there
15 minutes later
at w = 5.25 the total route is exactly 40. I can't think of any way to get it shorter though...:hmmm:
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dimis
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posted March 05, 2008 01:48 AM |
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Edited by dimis at 01:53, 05 Mar 2008.
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FOG-2 function
You might want to use GNUPlot to create similar plots like I plot.
For example in the last example I used the following commands:
Quote:
gnuplot> plot ((18+x)**2 + 31**2)**0.5 + ((6-x)**2 + 1)**0.5 title "FOG-2 function", 42 title "Bound"
If you want more 'tics' on x-axis, here you go:
Quote:
gnuplot> set xtics -100,1,100
gnuplot> replot
If you want to change the range for example as well:
Quote:
gnuplot> set xrange[0:10]
gnuplot> replot
Still your best solution seems to be 40 but you can do even better!! I don't know which x has the property and minimizes your function, but I have a good geometric interpretation (I believe).
edit: Seems that I was posting at the time you edited. Nice work so far!!! Let's see who will go below 40.
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Binabik
Responsible
Legendary Hero
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posted March 05, 2008 01:50 AM |
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I'm doing it graphically and haven't found anything shorter than 40 yet.
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dimis
Responsible
Supreme Hero
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posted March 05, 2008 02:05 AM |
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ooops...
I am laughing at myself. I guess you are right guys. I can not verify a solution less than 40. Seems that I made a mistake in the calculations when I first solved. Sorry about that. 
So, will someone draw a line of length 40?
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Binabik
Responsible
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posted March 05, 2008 02:08 AM |
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Yea, gimme a minute to make it and upload.
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Binabik
Responsible
Legendary Hero
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posted March 05, 2008 02:22 AM |
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Edited by Binabik at 02:33, 05 Mar 2008.
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Note that this solution is nearest to a 45 degree angle which gives you the shortest hypotenuse.
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Binabik
Responsible
Legendary Hero
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posted March 05, 2008 02:37 AM |
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Red is the shortest.
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dimis
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posted March 05, 2008 02:41 AM |
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Edited by dimis at 03:03, 05 Mar 2008.
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Nice! By the way, I just talked to the guy who gave me this riddle, and told me that the problem emerged since people wanted to minimize the ribbon (tape?) that is used in order to wrap a box containing whiskey, or a similar alcoholic beverage. Dunno if its true, but it's certainly interesting.
By the way, let's have a 3D-plot as well:
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Binabik
Responsible
Legendary Hero
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posted March 10, 2008 09:29 AM |
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Did anyone happen to notice that the triangle is a perferct 3,4,5 triangle?
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dimis
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posted March 10, 2008 10:25 AM |
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nope. Didn't check anything after I solved it. lol
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Duncan
Famous Hero
The Pathfinder
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posted July 18, 2008 12:32 PM |
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Hi guys, brought something interesting for you:
1 1 1 6
2 2 2 6
3 3 3 6
4 4 4 6
5 5 5 6
6 6 6 6
7 7 7 6
8 8 8 6
9 9 9 6
10 10 10 6
Make equalities from each line of the numbers above, for example (2nd row):
2 + 2 + 2 = 6 (I don't need to tell you this one is the easiest  )
Square etc. are welcome, but you cannot introduce new numbers as coefficient for example 1x2 + 1x2 + 1x2 = 6 --> this isn't allowed.
Let's see what you can come up with.
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But now I have come to believe that the whole world is an enigma, a harmless enigma that is made terrible by our own mad attempt to interpret it.
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Minion
Legendary Hero
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posted July 18, 2008 02:14 PM |
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3x3-3=6
4+4-sqr4=6
5=5x(-5+6)
6+6-6=6
7=7x(7-6)
cube root 8 + cube root 8 + cube root 8 = 6
9=sqr9x(9-6)
Hope some are right, don't know if cube roots were allowed (and didn't know what is the shortening used of it) Sqr = square root
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TheDeath
Responsible
Undefeatable Hero
with serious business
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posted July 18, 2008 02:19 PM |
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You can use cbrt for cube root
1*1*1 = 6^0
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Duncan
Famous Hero
The Pathfinder
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posted July 18, 2008 02:35 PM |
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Hehheh... you guys are fast
@Minion:
Yes, cube root is the only solution for that one, afaik. So it's taken
@TheDeath:
That one is fine too. But 1 = (1 x 1)^6 is more elegant, as it does not add any new number
The most interesting part is the last. Need to think out of the box for this one
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But now I have come to believe that the whole world is an enigma, a harmless enigma that is made terrible by our own mad attempt to interpret it.
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TheDeath
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Undefeatable Hero
with serious business
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posted July 18, 2008 02:39 PM |
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Edited by TheDeath at 14:41, 18 Jul 2008.
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log10(10) = (10/10)^6
log10 is the base10 logarithm
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Duncan
Famous Hero
The Pathfinder
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posted July 18, 2008 02:52 PM |
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Gah! Never thought that one is possible! 
When I played this, someone gave the answer the LHS being binary, and it was taken
Thx guys. It's all too easy after all
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But now I have come to believe that the whole world is an enigma, a harmless enigma that is made terrible by our own mad attempt to interpret it.
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