Adapted from MyRecipes.com and The Spirit:

1 (20-oz) can lychees in syrup, undrained
Crushed ice
1 cup unsweetened pink grapefruit juice
1/2 cup vodka
5 pink grapefruit sections

Drain the lychees in a colander over a bowl and reserve 1 cup of syrup. Discard the remaining liquid. Put one lychee in the bottom of each glass and fill each glass halfway with crushed ice. Combine the syrup, juice and vodka in a cocktail shaker filled with ice. Shake vigorously until chilled and strain into each prepared glass. Garnish each glass with a section of grapefruit.