  # 9 unit circles are packed into a square. What is the length of longest path connecting two opposite corners of square?

+1 vote
357 views

Nine unit circles are packed into a square, tangent to their neighbors and to the square. What is the length of the longest smooth path connecting two opposite corners of the square? Assumptions:
- The path must be continuous and follow the lines in the diagram; that is, it must be made up of portions of either the circles or the outside square.
- The path may not change direction suddenly.
- The path may not contain any loops.
- The path may not touch or cross itself at any point. posted May 15, 2017

+1 vote From the bottom end to the top the distance between the corners can be expressed as a sum shown below
1+π+π+(π/2)+(3π/2)+π+(π/2)+(3π/2)+π+(π/2)+1 = (2+ 17(π/2)). answer May 16, 2017

Similar Puzzles
+1 vote

Four semicircles are packed into a square, as shown. What proportion of the square is filled? In a unit square, two quarter circles are drawn, centered at two opposite vertices, What is the area of the oval-shaped region? In a square with a side length of 1, two quarter circles are drawn and a circle is inscribed between the quarter circles, as shown in the diagram.
What is the radius of the inscribed circle?   