Problem #PRU-35822

Problems Methods Invariants and semi-invariants Invariants Algebra and arithmetic Number theory. Divisibility Odd and even numbers Set theory and logic Theory of algotithms Theory of algorithms (other)

Problem

a) There are 21 coins on a table with the tails side facing upwards. In one operation, you are allowed to turn over any 20 coins. Is it possible to achieve the arrangement were all coins are facing with the heads side upwards in a few operations?

b) The same question, if there are 20 coins, but you are allowed to turn over 19.