Welcome to Namelandia, a realm where names hold great significance. In this land, a person’s name is a finite string using the Namelandian-alphabet, comprising 36 characters (coincidentally these are the English letters and the 10 digits).

The Namelandian people are renowned for their peaceful and kind nature. However, amidst this tranquility lies an ancient and peculiar tradition known as Namekilling. According to this tradition, if a Namelandian, let’s say xfd34cc, encounters another individual whose name is a sub-sequence of their own name, such as f34c, they are obligated to kill them immediately.

Given that there are infinitely many Namelandians, is it possible for them to exist without the looming threat of Namekilling? I.e. can they be named in such a way that no Namelandian’s name is a sub-sequence of another?

Formally - does there exist an infinite set of finite sequences over an alphabet of 36 characters, such that no element of the set is a sub-sequence of another?

The cover image for this puzzle was created by an amazing CG artist (and my father) - Nissan Leviathan. You can find more of his beautiful works here.

Spoiler Alert

Hint

No, Namekilling cannot be avoided, and in fact, a much stronger statement holds.