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Fill a large bowl with cold water. Squeeze the juice from one lemon wedge into the water.
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Trim the tops from the artichokes, then cut in half lengthwise, and place halves into the bowl of lemon water to prevent them from turning brown.
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Bring a large pot of water to a boil. Meanwhile, preheat an outdoor grill for medium-high heat.
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Add artichokes to boiling water, and cook for about 15 minutes. Drain.
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Squeeze the remaining lemon wedges into a medium bowl. Stir in the olive oil and garlic, and season with salt and pepper.
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Brush the artichokes with a coating of the lemon, olive oil, garlic dip, and place them on the preheated grill. Grill the artichokes for 5 to 10 minutes, basting with dip and turning frequently, until the tips are a little charred.
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Serve immediately with the remaining dip.