You have a twenty-sided die (a regular icosahedron) with an arrow on each face. You play a little game with the die. You place the die flat on the table. You rotate the die in the direction of the arrow on the top face. This step is repeated each time by looking at the arrow on the top face of the die. The game is over when you see the same arrow pointing in the same direction twice.
If you can choose the directions of the arrows and the starting position of the die, what is the longest this game can last?
What is the farthest the die can go from the start to the end of the game?