Place eggs in a saucepan and cover with water. Bring to a boil, remove from heat, and let eggs stand in hot water for 15 minutes. Remove eggs from hot water, cool under cold running water, and peel.

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Cut each egg in half lengthwise, remove the yolks, and place the yolks in a bowl with the mayonnaise, mustard, salt, and pepper. Mash the yolks and stir the mixture until smooth and thoroughly combined.

Fill each egg half with the deviled yolk mixture using a spoon, piping bag, or a sturdy plastic bag with a corner cut off.

Cut olives in half and place 1 half on each filled egg as the spider body. Cut the other olive half into 4 strips. Cut each strip in half, so you end up with 8 thin olive pieces for the legs. Arrange 4 olive legs on each side of the spider body. Dust with paprika.