You're supposed to head down to the beach south of Fuchsia City, and use Surf. Continue down the waterway, and you'll eventually find an island. These (this?) are the Seafoam Islands. You'll need plenty of health restorers, and possibly a lot of Ultra Balls. This is where Articuno can be found. After you get out of there, continue west until you find another piece of land. This is Cinnebar Island. This is where you will have your next gym battle. But you'll need to find the key first~
Look in the mansion. And remember, have fun with it!
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Soul Badge (Fuchsia Gym)
You need to defeat Koga in Fuchsia City to get the 5th badge, the Soul Badge.
In Pokemon Red, the fifth badge is possessed by the Poison-Type Koga. The badge is named Soul Badge. It lets you use Surf outside of Battle.
The 8 badges for Pokemon Red are: Boulder Badge, (Brock) Cascade Badge, (Misty) Thunder Badge, (Lt. Surge) Rainbow Badge, (Erika) Marsh Badge, (Sabrina) Soul Badge, (Koga) Volcano Badge, (Blaine) and Earth Badge. (Giovanni)
U win