Ann probably went to the store for more eggs. Surely she will try ALL of the methods presented to determine once and for all which is best
A good pot is essential - so if you don't have good stainless steel cookware, then a trip to the potshop is in your future.
Method #1 - Preferred method
Use eggs that have been in the fridge for several days - they will peel easier
Place eggs in pot - with or without the paper towel - I have TowneCraft and I have used paper towels with success.
Cover eggs with cold water - filtered is best
Add a glug glug of vinegar and a pinch of baking soda
Put on stove and turn on medium
When water comes to a full roiling boil, add a dash of salt
Let eggs boil for 5 minutes
Turn off stove and let eggs cool in the water - they finish cooking
This is important -- use one egg to crack another - tap them against each other
The shells should almost fall off under running water Method #2 is what I use when I'm in a hurry --
Place eggs in pan, fill with hot tap water
Turn burner on high
Go in sewing room and forget eggs
Run to kitchen saying bad words when the eggs explode due to all the water evaporating and the eggs cooking over high heat in dry pan
Toss exploded eggs and clean stove
Scrub pan
Retry using Method #1