I’m not sure if children still play Cat’s Cradle---a game which only required a piece of string. Nimble fingerwork allowed one to create some clever patterns of interwoven lines. Structures that could be passed from one pair of hands hands to another as they morphed and inverted to create new shapes. It’s one of those games that feels a bit too old-fashioned and innocent to keep modern generations entertained for too long. This puzzle is inspired by Cat’s Cradle games I remember playing as a child.
Four nails are hammered into a board to form a square of side L. One end of each of four identical linear elastic bands of natural length L ⁄ 2 are knotted together, and the free ends placed over the nails to form a cross within the square. By symmetry, the knot E is co-incident with the center of the square O. A fifth identical elastic band is added between the knot and one of the nails. What is the resulting separation between E and O?