I recently had the occasion to attend a workshop on Japanese bookbinding, which utilizes a strong thread to 'sew' the back of the book together. This technique is very different from that used in Western books. There are an enormous number of variations on the 'lacing' pattern used to sew the book together, but most of them seem to have some reasonable degree of symmetry -- e.g., the pattern on the back of the book is the mirror image of that on the front. The rules are somewhat different from that used in shoes -- you can have multiple parallel rows of 'eyelets', and you can thread through an eyelet multiple times. What intrigued me was the possibility that there may be some relationship with Euler Circuits in undirected graphs and the K\"onigsberg bridge problem. I started my bookbinding by following the teacher's directions, but then speculated that a 'greedy algorithm' would work. When the teacher made a mistake and got stuck, the greedy speculation was proved false. But I was still struck by how hard it was to 'get stuck'. I suspect that some Japanese mathematician has already studied this problem, but I also suspect that the paper is published in Japanese. Here is the relevant theorem from graph theory: Theorem (Euler?). An undirected graph possesses an Euler circuit iff it is connected and its vertices are all of even degree.