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In a medium saucepan, mix sugar, flour and salt. Stir in 1 cup of milk, mix until smooth, and bring to a boil over medium heat, stirring constantly. Continue to stir until smooth and thickened, about 2 minutes, then remove from heat.
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Return saucepan to the heat and bring to a boil again, stirring constantly, lower heat and simmer until mixture thickens a bit more, about 1 minute.
Remove from the heat and stir in butter and vanilla. Cool slightly and pour into the baked pie shell.
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