The jumps of the bunny

Discrete Mathematics Level 4

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.


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