Mathematicians discover the worst way to hang a painting

In 1997, mathematician A. Spivak posed a riddle about hanging a painting on two nails so that removing either nail would cause it to fall. This sparked interest in a broader set of picture-hanging problems, where mathematicians explore complex ways to hang paintings that involve intricate string arrangements. Retired computer scientist Tom Verhoeff and others have worked on these problems, reducing the complexity of solutions. For instance, they tackled a problem where a painting falls if any two of four nails are removed, reducing the solution from 80 to 16 string wraps. These problems connect to advanced mathematical concepts like group theory and graph theory. While the practical use of these problems might be questioned, they offer insights into mathematical theories and have applications in fields like cryptography and voting theory. QUESTION: How might exploring seemingly impractical problems, like complex picture-hanging puzzles, benefit our understanding of mathematics and its applications in real life?