Graphs are everywhere. In discrete mathematics, they are structures that show the connections between points, much like a public transportation network. Mathematicians have long sought to develop ...

For example, 6 contributes 6 when it’s in an undoubled position, and it contributes 3 from a doubled position because 6 doubled equals 12 and 1 + 2 = 3. Messing up a single number while typing your ...