Cooking with Dee

I made hard-cooked (many of you call them hard-boiled) eggs the other day.  I placed them in cold water to cover and waited ten minutes or so then turned on the timer for ten minutes.  Now, after cooling, the shells are difficult to remove and the yolks are OK for me but only 90% done for most people.  They’re not runny, just dark yellow in the center and tough to peel.  Is there a magic number of minutes at 7,500 feet above sea level for the perfect egg?  I was thinking the entire time that all the time it took for them to come to a boil, they’d be over-cooked!  Please let me know.  Thanks, Dee