Exact shortest walking order through the 9 park-core gyms at Murray Park, on real path-network distances (BRouter). Solved with Held–Karp and confirmed by exhaustive brute force — 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 Caring for reference. The line runs Parks & Rec → Supportive and skips the closing leg.
The north trio. The LDS church, Playground, and Batting Cage were dropped from routing — Playground alone added 3.87 km to the loop (Mick Riley Golf Course blocks the direct line and the gym sits in a private enclave only reachable from 4800 South or 900 East). They stay plotted in red; Playground, Desert Star Playhouse, and Dog And Cat sit outside the default frame — zoom out to see them.
Park lawns. BRouter won't cross grass: four intra-park legs are overstated (worst: Supportive ↔ Soccer Field — routed 391 m, ~74 m straight across an open pitch). Cutting them saves ≈ 0.12 km and shuffles the middle of the order. Plotted totals are the stay-on-paths upper bound.
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.