Answer:
Salt.
put a couple of pinches of salt per dozen in the water pre-boiling.
Link to column: What’s the secret of getting hard-boiled eggs to peel easily?
Two mentions in that column that eggs at least a few days old are easier to peel than fresh-from-the-chicken eggs. E.g.,
So I would expect that Hundred Year Old eggs should be easy peasy to peel.
My experience confirms that a freshly boiled egg peels best when you chill it with cold water. But I have also found the opposite to be true. If I take a boiled egg that’s been sitting in the refrigerator for a while, it peels best after I have held it under a stream of hot water for a few seconds.
There was a method J.P. Gumby used for arranging chrysanthemums that can also be used for unpeeling 8-minute eggs.
I struggled with this important issue for years before stumbling on a 2-step method that always works for me:
(1) Allow eggs to sit unrefrigerated for a few hours so they reach room temperature throughout.
(2) Immerse for about 10 minutes in initially already vigorously boiling water. Water temp may be reduced to 1/2 highest setting after a couple of minutes.
Pretty much what I do except I turn off the heat after the eggs go in and they sit 18-20 min.
Break shells and into ice water.
I just make sure to let them cool–maybe even running cold water over them to facilitate this. Then I break them in a specific place: that more flat bottom where there’s always an air bubble, giving you a lot of room to get under the shell. From there, it always peels easily.
Hm- I’ll try this since it would save quite a bit on the energy usage.
TY for the tip.
Hot eggs shell easily when cooked using the method I describe in reply #6.
If you do a lot of hard boiled eggs, consider doing them in a pressure cooker. I do a dozen at a time and they will peel with no effort straight from the fridge.
There are many automatic electric ones now that do a great job. I have an InstaPot. I put the eggs in, set the timer for 1 minute at pressure, and the cooker does all the work.
One other thing that helps is to tap the boiled egg against the countertop in various places (on the egg, not the countertop) so it’s lightly cracked all over. Then roll the egg around between your palms to loosen the shell. I do this in addition to cooling the eggs with cold water after cooking, and the shell (usually) slides off easily.
you all are working way too hard on this : )
As someone who used to need to boil and prep dozens of hard boiled eggs daily, the method is simply to put eggs in pot, cover eggs with water (with extra water for evaporation while cooking), and dump in a heavy dash of salt.
when done, of course run under cool water, though eggs will still be warm (hot) to touch, and shells will easily unwrap in your hands, even if you put them into refrigeration for storage for later use/shelling.
without the salt in the water, you can play rinse games all day - and still at least 2/3 of your eggs will break apart when peeling, and shells will be like glue to the whites.
Basically what I do. The vigorously boiling water also keeps the eggs in constant motion so that the yolks don’t settle to one side of the egg and are more centered when the egg is hard which helps a lot when making deviled eggs.
I also plunge them in ice right after. Being lazy, I dump out the hot water, replace it with cold water, toss in some ice cubes and put the pot and eggs in the fridge. After some ambiguous amount of time I take out the pot, pour out the water and shell the eggs. I almost never have any that are difficult to shell.
I love deviled eggs so I do this very often. 
I don’t ever salt the water. I don’t imagine that has any effect on the eggs, since the shell keeps all the salt out. (If it didn’t then salting the water would make the eggs saltier, and it won’t.) What salting the water can do is cause the water to boil faster, but you have to add a lot of salt.
I’m just surprised that this was the subject of a staff report. It’s been thoroughly covered in CS threads in the past.
I’ve tried just about everything. I’ve found that there is no solution that always works, but it often helps to add a teaspoon of baking soda to the water. Old eggs vs. new eggs rarely makes a difference. Soaking in ice is necessary to stop the cooking process exactly where you want; it does little if anything to help with peeling.
I have found that the cheapest eggs also work the best for hard boiling, the organic, holistic, free range whatever higher level of egg it is is much harder to peal.
You have to cook them way longer if you want them to peal.