Whats an elegant way to tour a hypercube, in distance order:
For all $k=1, \dots, n$, you can easily generate all bit strings of length $n$ with exactly $k$ bits set.

The lexicographically smallest bit string has the $k$ ones in the $k$ least significant bits. If you interpret this string string as an integer, and it fits in a constant number of words, you can use bit tricks to find the next string in a constant number of operations.

See the section "Compute the lexicographically next bit permutation" here, and this answer for an explanation.