How can I cook an egg to win at egg tapping? Easter is coming up, and I was wondering how I should prepare eggs to be as strong as possible for a game of egg tapping?

The egg should still look and feel like a regular egg (although it's probably painted, because, y'know... Easter).

This is a cooking question, so I'm looking for answers about the cooking process, not about modifying the egg afterwards (e.g. coating with something hard).

Bonus points if the egg is still edible after I've beaten all my in-laws!
To keep this on topic, I'll focus on ingredient selection and preparation, any further hints are a physical aspect and have to do with where to hold and how to hit.

Your first goal is to find an egg with a very hard shell:


This means, find an egg from a rather young (max. 6 month old) chicken. The thickness of the shell decreases naturally during the 1-1.5 years a chicken is typically kept for egg production.
Chickens that have access to the outside and that pick up a lot of sand, grit and small stones and have a very diverse feed with a generous access to grains plus supplements like oyster shells, will produce the hardest shells.
And, little known, green eggs (from the so-called Easter Egger breeds) have a thicker and harder shell than white eggs. Bonus: you can skip the coloring step...


All eggs are harder when hard-boiled (compared to raw): 


Just avoid anything that weakens the shell, so no vinegar in the cooking water or the colouring liquid. Use natural dyes (as opposed to the commercial products where you dip a cooked egg in a vinegar-water-dye solution). Likewise, do not wash the eggs unless absolutely necessary, the natural protective layer should also prevent weakening the shell.
I would also avoid mechanical stress, so bring your eggs to room temperature and use the cooking method where you put the eggs in cool water, bring them gently to a (near) boil and let stand in the covered pot off the heat for fifteen minutes or so. In this case, I'd probably rather have the green ring around the yolk than a semi-soft egg.