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Heart Gold and Soul Silver: Game World Pokemon
Throughout Heart Gold and Soul Silver there are many non-Legendary Pokemon that you can find in the overworld, instead of random encounters. Here are those Pokemon.

Sudowoodo
Sudowoodo
Lv. 20
You can find Sudowoodo on Route 36, north of Goldenrod. You need to defeat Whitney and then get the SquirtBottle from the flower shop. Sprinkle the Sudowoodo with water to initiate the battle.

Shiny Gyarados
Shiny Gyarados
Lv. 30
Shiny Gyarados is in Lake Rage. You need to deal with him, either catch or knock out, in order to progress through the story.
This is the only shiny Pokemon encounter guaranteed in Heart Gold and Soul Silver.

Lapras
Lapras
Lv. 20
Lapras is found in the basement of Union Cave on Fridays. Lapras will always appear each Friday no matter how you dealt with it last Friday. If you catch a Lapras on Friday, a new Lapras will show up the next Friday. Conversely, if you knock out Lapras on Friday, another one will still show up the following Friday.

Snorlax
Snorlax
Lv. 50
Snorlax is located east of Vermillion City. In order to wake up Snorlax you need to play the PokeFlute over the radio. In order to fix the Kanto Radio Station you must fix the Power Plant, which means you need to get a missing part from Cerulean City. Travel to the Golden Bridge in Cerulean city and defeat the Team Rocket member hiding in between two people. He will tell you the missing part is in the Cerulean Gym. Find the missing part hidden in the top set of inner tubes and head back to the Power Plant to restore the power. Once you restore power to the radio station go back to Snorlax and open your PokeGear and select your radio. The PokeFlute is located in between the top two stations at the top of the circle. Once the PokeFlute is playing exit your PokeGear and talk to Snorlax to initiate the battle.