i’m pretty sure i have the infinite quarter sequence figured out..
*remove 20 coins from the infinite pile, thus making 2 separate piles.
*flip the 20 coins from your chosen pile.
*leaving you with a pile of 20 tails quarters, and the infinite pile with the original 20 tails quarters still floating around.
not sure this is the right answer, but its the only thing i could come up with.. the chances of you picking any of the original 20 tails quarters out of an infinite pile of heads is highly unlikely, and the chances of grabbing 20 heads quarters is infinite, so once you flip your chosen 20 (of presumably heads), you now have your pile of 20 tails, and the other pile of quarters with the original 20 tails still there.
if you throw in the idea of possibly getting even 2 tails (or 1, 3 ect..) in your chosen 20, once you flip the coins it will leave you with 18 tails 2 heads, and 18 tails in the original pile.. leaving with equal amount of tails in each pile.