# The jumps of the bunny

**Discrete Mathematics**Level 3

A one year old bunny is sitting on the number 0 in the number line. His father, Bugs Bunny, is waiting for him on the number 10.

The bunny has to reach his father. At each minute, he can:

- Move one step forward;
- Move two steps forward;
- Stay still;
- Move one step backward;
- Move two steps backward.

There are \(N\) possible ways the bunny can be on the number 10 after 10 minutes. Find the last three digits of \(N\).

**Details and assumptions**

The bunny is allowed to hop beyond 10, and then come back.

There are no restrictions on the bunny entering the negative numbers. The bunny can go as much backwards as he wants.

Order does matter. For example, the steps \(\{0000022222\}\) and \(\{2020202020\}\) are considered distinct.