In the 1950s, a Scottish mathematician named C. Dudley Langford looked at a stack of six blocks his young son had assembled (see Endnote #1) and noticed something interesting that would lead him to the mathematical discovery he’s remembered for today.
Langford noticed that between the two red blocks was one block, between the two blue blocks were two blocks, and between the two yellow blocks were three blocks. Being a mathematician, Langford immediately wondered “Could we do this with more than three colors?”
Can you figure out how to add two green blocks and arrange the eight blocks so that there will be one block between the red blocks, two blocks between the blue blocks, three blocks between the yellow blocks, and four blocks between the green blocks?
And, having succeeded with four colors, can you do it with five?Continue reading