The scene seems doomed to trial and error: you know how many coins are face up, but you can't recognize any by touch. The surprising thing is that the solution does not depend on identifying anything, but on a gesture that transforms ignorance into symmetry.
The 100 coins blind
Riddle statement
There are 100 coins on a table. You know that exactly 20 are face up and 80 are face down, but you are completely in the dark and cannot tell one from the other by touch.
You can separate coins into two piles as you want and also turn over the coins as you need.
Can you make two piles so that both have the same number of face up coins?