MathLapse: String vs Beads
“Stringing” a 3-dimensional integer lattice of “beads” with a Hamiltonian path (one that crosses every vertex but only once) as a visual showcase of 1-1 correspondence with the integers.
This is a bit like the Aleph-Null version of how Space-filling curves were discovered after Cantor’s surprising proof that the continuum of unit interval has the same cardinality as that of the unit cube.
I imagine this as a sequence of progressive challenges between String and Beads (1 row, 2, 3… infinite rows; 1 plane, 2, 3… infinte planes). The surprise twist would of course be an extra challenge of String and Necklaces (the infinite necklaces of black & white beads).