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Drawing a long line


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#1 BMAD

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Posted 23 October 2013 - 04:37 PM

Suppose you have a single sheet of an 81/2" x 11" paper.  Your task is to draw the longest continuous line possible using an EXPO marker that has infinite ink.  The line can curve but it cannot be picked up off the paper or overlap and of your previously drawn line.  Since you are drawing a line with a marker, your line has a defined width.  For the sake of argument, presume your line width is 1 inch.  What is the longest possible line that can be drawn?


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#2 ralfvin

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Posted 23 October 2013 - 07:21 PM

Drawing a continuous line beginning at the edge of the paper running down the length and then making a 90 degree turn at each corner without crossing the line will yield the following lengths in inches before you run out of space. The total length is 91.5 inches. 

 

11
7.5
10
6.5
9
5.5
8
4.5
7
3.5
6
2.5
5
1.5
4
 

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#3 bonanova

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Posted 23 October 2013 - 07:51 PM

Spoiler for looks like

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#4 shammaa

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Posted 23 October 2013 - 09:49 PM

Actually, I think newbie has the right idea, but numbers are off a little...so the answer would be:

Spoiler for answer


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#5 austinm

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Posted 24 October 2013 - 02:18 AM

Spoiler for in the hypothetical third dimension


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#6 DeGe

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Posted 24 October 2013 - 11:03 AM

Spoiler for looks like

Agree! Another Aha puzzle.


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#7 bonanova

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Posted 26 October 2013 - 04:48 AM

 

Spoiler for looks like

Agree! Another Aha puzzle.

 

 

But still ... if I had to pick the most satisfying approach, I would define (zero-width) line segments that run midway from the edges of the 1-inch line, and then sum their lengths. I think this was the approach taken in previous posts. Or, take the average of the left and right edges of the 1-in-thick line.


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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#8 BMAD

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Posted 26 October 2013 - 05:38 AM

Would the solution change if we consider that the initial mark is from a curved end and not square?  

 

like the picture below:

 

Marker-Pen-Close-Up-006.jpg

 

 


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#9 Japes

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Posted 26 October 2013 - 12:38 PM

After filling in the first side and ending up in the centre of the paper sheet bring the corner of the sheet close to the pen and without removing the pen from the paper move the pen onto the reverse side. Then fill in the second side giving a total length line of about 176 inches.
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