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 question. Four men A,B,C,D pass a ball. On each pass the holder chooses one of the other three men. A holds it initially. How many passing sequences leave A holding it after the sixth pass? Examples: $A\to B\to C\to A\to D\to B\to A$ and $A\to D\to C\to B\to D\to B\to A$.
Optional bonus question. Four men A,B,C,D pass a ball. On each pass the holder chooses one of the other three men. A holds it initially. How many passing sequences leave A holding it after the sixth pass? Examples: $A\to B\to C\to A\to D\to B\to A$ and $A\to D\to C\to B\to D\to B\to A$.