You have been invited to an $n$-dimensional universe, where $n$ is an integer greater than $1$.
Here, matchsticks are idealised lines of unit length, and they can pass through each other.
They want you to construct a ruler for them. (Never mind that they are already rulers themselves of this universe.)
A ruler consists of a structure made out of matchsticks (of unit length). Matchsticks can be stuck together at their ends (with magical glue). Every pair of endpoints which are rigid with respect to each other can be used to make a measurement.
For example, when $n=2$, two equilateral triangles are affixed together, the $2$ furthest endpoints are rigid with respect to each other, and can measure a distance of $\sqrt{3}$.
You are not limited in the number of matchsticks you want to use in your ruler, the more matchsticks, the grander the ruler, of course.
Of course, a ruler would be useless if it could not measure lengths. What sort of lengths can your ruler measure, for each number of dimensions?