I Love This Sudoku Example, but I Don't Understand Why Would You Need Any Cards Face Up or Face Down?

The Sudoku example actually has an interactive and an on interactive version. In, in some time as well in the 80s, there was a method developed that let, let you transform interactive proofs into non-interactive Proofs. So by having cryptographically secure hash function, you basically use a hash function to generate randomness or to like create, like to pick challenges in this protocol. The face up ones are important to show that you're solving this particular puzzle.