Question 30
If the answer is not an integer, give the nearest integer. If the calculated answer has more than five digits, give its last five digits.
Optional bonus. Four men A,B,C,D pass a ball; each holder passes to one of the other three. A holds it initially. How many sequences leave A holding it after the seventh pass? Examples: $A\to B\to C\to A\to D\to B\to D\to A$ and $A\to D\to C\to B\to D\to B\to D\to A$.
Optional bonus. Four men A,B,C,D pass a ball; each holder passes to one of the other three. A holds it initially. How many sequences leave A holding it after the seventh pass? Examples: $A\to B\to C\to A\to D\to B\to D\to A$ and $A\to D\to C\to B\to D\to B\to D\to A$.