Cutting the mangoes: Peel the mangoes, then cut the flesh from the pits: A mango pit (to which the flesh clings tightly) is flattish and oval, more-or-less a smaller version of the mango's overall shape. To cut the flesh off the pit, stand a mango on one end and slice the flesh from one side of the pit. Turn the mango around and slice the flesh off the other side. You'll be able to get a couple thin slices of flesh off the pit on each end. Cut the large pieces into long 1/2-inch-wide "fingers."
Salad: In pointed Sno-Cone cups (you'll need a snow-cone holder or a glass to support each cup) or in paper cups or glasses, combine a portion of mango, jicama and cucumber "fingers" or wedges (they will be standing in the cups). Mix the chile and 1/2 teaspoon salt; sprinkle over the "salads." Serve with lime wedges for each guest to squeeze over the pieces as they eat them.
Variation: Cut the mango, jicama and cucumber into cubes instead of "fingers," and mix together in a large bowl. Juice the limes (rather than cutting them into wedges) and drizzle over the mixture. Sprinkle with the salt and chile, and serve on a buffet or pass this at the table.