1) What is the maximum number of 9×9 Sudoku puzzles equivalent to a given one? (Defining “equivalent” properly is part of the problem).
2) You are playing a computer game where you have to get out of a finite maze by a sequence of arrow keystrokes (up, down, left, right). You are guaranteed that there are no dead ends: from any point in the maze there is a way out. Reversing your previous move does not always get you back to the same place because the passages are twisty. The monitor breaks and you can no longer see where you are, but you can keep pressing arrow keys and the computer will beep if you have escaped. Is there a strategy to guarantee you eventually get out?