Question 1142265
<pre>
I think somebody is forgetting that the elastic band 
has straight parts and round parts.

OK, maybe they took the pencils to be hexagonal in cross-section
and not circular.  I have both kind in my pencil collection.

Anyway I took the pencils to be circular in cross-section.

The elastic band is in green:

{{{drawing(400,400,-7,7,-7,7,

circle(0,0,2), circle(-4,0,2), circle(4,0,2),
circle(-2,2sqrt(3),2), circle(2,2sqrt(3),2),
circle(-2,-2sqrt(3),2), circle(2,-2sqrt(3),2),
green(

arc(2,2sqrt(3),4.15,-4.15,30,90),


line(-3.69,4.5,-4-sqrt(3),1),


line(-2,2sqrt(3)+2,2,2sqrt(3)+2),
line(3.69,4.5,4+sqrt(3),1),

line(-2,-2sqrt(3)-2,2,-2sqrt(3)-2),
line(3.69,4.5,4+sqrt(3),1),

line(3.69,-4.5,4+sqrt(3),-1),

line(-2,2sqrt(3)+2,2,2sqrt(3)+2),
line(-3.69,-4.5,-4-sqrt(3),-1),

line(-2,2sqrt(3)+2,2,2sqrt(3)+2),
line(3.69,4.5,4+sqrt(3),1)) )}}}

There are 6 straight parts and 6 round parts to the elastic band.

Each straight part is the length of two radii, as we see by this
red rectangle. which is 1 diameter or 7mm.  So the 6 straight
parts amount to 6×7mm or 42mm.

{{{drawing(400,400,-7,7,-7,7,

circle(0,0,2), circle(-4,0,2), circle(4,0,2),
circle(-2,2sqrt(3),2), circle(2,2sqrt(3),2),
circle(-2,-2sqrt(3),2), circle(2,-2sqrt(3),2),
green(

arc(2,2sqrt(3),4.15,-4.15,30,90),


line(-3.69,4.5,-4-sqrt(3),1),


line(-2,2sqrt(3)+2,2,2sqrt(3)+2),



line(3.69,4.5,4+sqrt(3),1),

line(-2,-2sqrt(3)-2,2,-2sqrt(3)-2),
line(3.69,4.5,4+sqrt(3),1)),


red(line(-2,2sqrt(3),2,2sqrt(3)),
line(-2,2sqrt(3),-2,2sqrt(3)+2),


line(-2,2sqrt(3),2,2sqrt(3)),
line(2,2sqrt(3),2,2sqrt(3)+2)),

line(-2,2+2sqrt(3),2,2+2sqrt(3))),green(


line(3.69,-4.5,4+sqrt(3),-1),

line(-2,2sqrt(3)+2,2,2sqrt(3)+2),
line(-3.69,-4.5,-4-sqrt(3),-1),

line(-2,2sqrt(3)+2,2,2sqrt(3)+2),
line(3.69,4.5,4+sqrt(3),1))) )}}}

And as you can see by the 60° red sector,

{{{drawing(400,400,-7,7,-7,7,

circle(0,0,2), circle(-4,0,2), circle(4,0,2),
circle(-2,2sqrt(3),2), circle(2,2sqrt(3),2),
circle(-2,-2sqrt(3),2), circle(2,-2sqrt(3),2),

red(line(2,2sqrt(3),3.69,4.5),line(2,2sqrt(3),2,2sqrt(3)+2)),



green(

arc(2,2sqrt(3),4.15,-4.15,30,90),


line(-3.69,4.5,-4-sqrt(3),1),


line(-2,2sqrt(3)+2,2,2sqrt(3)+2),
line(3.69,4.5,4+sqrt(3),1),

line(-2,-2sqrt(3)-2,2,-2sqrt(3)-2),
line(3.69,4.5,4+sqrt(3),1),

line(3.69,-4.5,4+sqrt(3),-1),

line(-2,2sqrt(3)+2,2,2sqrt(3)+2),
line(-3.69,-4.5,-4-sqrt(3),-1),

line(-2,2sqrt(3)+2,2,2sqrt(3)+2),
line(3.69,4.5,4+sqrt(3),1)) )}}}

Each round part of the elastic band is 1/6 of a circumference
of one of the circles.  And there are 6 of them, so all 6
total to one circumference of each circle, which is {{{pi*7mm}}}

So the answer is 6 straight parts which is 42mm plus 6 round
parts which is {{{7pi}}} mm.

Answer {{{42+7pi}}} mm.

Edwin</pre>