Question 242392
If there are 10 squares that have 15ft long sides, and they can share sides, what is the least amount of wire needed to construct all 10 sauares?
<pre><font size = 4 color = "indigo"><b>
10 squares can be drawn in 3 dimensions by constructing
this "chair" using 22 line segments.  Since each line 
segment is 15ft long, the minimum amount of wire needed 
is 22x15 or 330 ft.  3 line segments cannot be seen 
in the drawing as they are back behind the bottom cube.

{{{drawing(320,400,-2,2,-1,4, 

line(0,0,1,0),
line(1,0,1,1),
line(1,1,0,1),
line(0,1,0,0),
line(0,0,-.7,.4),
line(-.7,.4,-.7,1.4),
line(-.7,1.4,0,1) ,
line(-.7,1.4,.3,1.4),
line(.3,1.4,1,1) ,
line(1,1,1,2),
line(1,2,.3,2.4),
line(.3,2.4,-.7,2.4),
line(-.7,1.4,-.7,2,4),
line(-.7,2.4,.3,2.4),
line(.3,2.4,.3,3.4),
line(.3,3.4,-.7,3.4),
line(-.7,3.4,-.7,2.4),
line(-.7,1.4,-.7,2.4),
line(0,1,0,2), line(0,2,-.7,2.4), line(.3,1.4,.3,2.4)

 )}}}

If this must be done in 2 dimensions I think the minimum 
number of segments is 27, and 27x15 or 405 ft. of fencing would
be needed.

{{{drawing(400,400,-1,5,-1,5,

rectangle(0,0,3,3), rectangle(1,0,2,3),
rectangle(0,1,3,2), rectangle(3,2,4,3) )}}}



Edwin</pre>