The guard in the gate has a favor to ask. Deliver his Spearow's piece of mail to the man by the pond on Route 31, and the man will reward you with TM50 (Nightmare). Return here to receive an HP Up from the guard as thanks.
Speak to the woman with her Persian to get a Quick Claw, which sometimes allows slower Pokémon to attack first. On the far side of the park, there is a break in the fence near the east entrance. Look around the exterior of the park to find a Parlyz Heal and TM28 (Dig), then leave through the east gate to reach Route 36.
The contest is free to enter, and the objective is to catch the single best Bug Pokémon possible. Trainers are given 20 Park Balls and allowed to use a single Pokémon from their party. The others are held temporarily until the competition is over. Any Pokémon caught during the contest will be recorded by the Pokédex, though only one can be kept for judging. The Pokémon that was judged may be kept after the competition.
A colored background means that the Pokémon can be found in this location in the specified game. A white background with a colored letter means that the Pokémon cannot be found here.
The tiny Route 36 is a unique stretch of land, the only route to link five different locations together. East of the park, that odd tree is still blocking the narrow trail from every direction. Try watering it with the SquirtBottle, and it attacks! It turns out to be a Sudowoodo, a Pokémon more akin to a rock than a tree. Once the path is clear, talk to the guy near Violet City to receive TM08 (Rock Smash), as thanks for removing the troublesome Pokémon.
On Thursdays, Arthur can be found in the northeast part of the route. Meet up with him to receive a Hard Stone, which enhances Rock-type attacks.