In a large bowl, combine the popcorn and gumdrops.
In a medium saucepan, combine sugar, corn syrup, butter, and salt. Bring to a boil, and cook over medium heat for about 5 minutes, stirring constantly. To test doneness of syrup, drizzle a small amount in ice water. If it immediately becomes brittle, syrup is sufficiently cooked. Remove from heat, and add to popcorn mixture; mix well.
Rinse hands in cold water, and form the mixture into ten 2- to 3-inch balls. Place on wax paper and cool for 15 minutes.