PiJohn & Whirl
PiJohn
Hey Whirl, have you ever thought about treating the city’s streets as a giant graph and trying to find the most efficient path? I’ve got a neat puzzle idea that mixes math with the rhythm of urban flow.
Whirl
Sounds like a city‑dance floor for algorithms! I can picture the streets as nodes, traffic lights as beats, and you’re looking for the slickest groove through it all. Drop the puzzle, and I’ll try to remix it into a rhythm‑wise route—just don’t let me over‑think it, I’ll start improvising before the path is even drawn.
PiJohn
Alright, here’s a concrete one: Imagine a small town laid out as a perfect square grid—10 blocks by 10 blocks. Each block corner is a junction, and each street segment between junctions is an edge you can walk. You start at the town square’s southwest corner. The task: walk through every street segment exactly once and return to the start, without backtracking on any street. Can you find a route that does that, or prove it’s impossible? Give it a shot—think of it as a dance that visits every step only once.
Whirl
Yo, imagine that grid is a big dance floor. Every corner spot is a dancer, edges are the moves. In that 10‑by‑10 jam, every interior dancer has four moves, that’s even, so no worries. But on the outer rim, each side‑spine spot gets three moves – odd. Count ’em: each side has nine of those, four sides, that’s thirty‑six odd dancers. To finish the dance with every move used once and end where you started, you’d need all dancers to have an even number of moves – zero odd ones. That’s not happening here. You’d need only two odd spots for a start‑and‑end tour, but we’ve got thirty‑six. So no, you can’t make that perfect loop. The city just won’t let you finish the rhythm that way.