Exact shortest walking order through 19 selected gyms in Liberty Park, Salt Lake City, on real path-network distances (BRouter). Solved with Held–Karp (in C) and independently re-proven — provably optimal for the routed distances. Every gym within ~1 km of the route is plotted in red for context but excluded from routing — zoom out to see them all.
routed walking path ● routed gym ● gym not on route ● start / endpoints ◌ 80 m reach scroll to zoom · drag to pan · double-click to reset
Loop or line? The loop returns to the start; start at any gym — numbering is anchored at Eagle Fountain for reference. The line runs 石狮子左 (west edge) → Campsite Creative and saves 447 m over the loop.
Verified. An independent from-scratch Held–Karp in C reproduced both totals exactly, and the matrix audit passed every hard check. The big detours are real: the fenced tennis complex, Liberty Lake, and the Rotary playground block their straight lines.
Park lawns. Nine short legs in the open NE quadrant are overstated where BRouter follows the sparse path grid instead of cutting grass — but only ≈135 m of the loop (3%) is artifact. Cut the lawn there and you beat the estimates by ~2–3 minutes.
Selection. From the 40 closest gyms, everything west of the stone lion, south of Rusted Metal Couple Sculpture, east of the 2002 Games Rock Bench, or north of Cummings Studio Chocolates was excluded from routing but kept on the map; Rock Bench, Rusted Metal, and Cummings were dropped in a second pass.
Method. Distances are the per-pair minimum of BRouter's hiking-mountain and shortest profiles plus a metric-closure pass. Gym data: PokeScrapper capture through 2026-07-07. Buildings and paths: OpenStreetMap.