1. Mix together water and blue food coloring in a large bowl and set aside.
2. Lightly tap the eggs with a spoon to crack the shell. Do not remove the shell.
3. Place the unpeeled, cracked eggs in the water and food coloring mixture and refrigerate for at least 2 hours, or until completely cold.
4. Remove the eggs from the refrigerator, peel carefully, and cut eggs in half lengthwise.
5. With a spoon, gently scoop out the egg yolks and transfer to a bowl.
6. Place the whites aside, while you prepare the yolks.
7. Take the bowl with the yolks, and mix in the mayonnaise, mustard, salt, and pepper. Mash the mixture together until it is smooth and thoroughly mixed.
8. Using a piping bag, or a plastic bag (with the corner cut off), pipe the yolk mixture into the egg whites.
9. Note add the spiders! Cut each olive in half, and place 1 half on each filled egg, this is the "spider body". Taking the leftover halves, cut each half into 4 strips, then cut each strip in half. You will end up with 8 thinly slices olive pieces for the spider's legs. Arrange the legs on each side of the spider's body.

OPTIONAL: Dust with paprika for an added kick!