Let's throw several dice at once. Throw away the dice with 1 eye, throw only the remaining dice again, and throw away the dice with 1 and repeat it until there is no dice left.

Let's start with three dice, and let's say the number of dice left after the nth throw is Xn.

1. Does Xn satisfy Markov's properties?

2. Find the previous matrix.

3. Find level 3 status vector.

4. How many dice do you expect to have after 3 dice are thrown?