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  1. Find a recurrence relation for the number of ways to completely cover a $2 \times n$ checkerboard with $1 \times 2$ dominoes. [Hint: Consider separately the coverings where the position in the top right corner of the checkerboard is covered by a domino positioned horizontally and where it is covered by a domino positioned vertically.]
  2. What are the initial conditions for the recurrence relation in part $(A)?$
  3. How many ways are there to completely cover a $2 \times 17$ checkerboard with $1 \times 2$ dominoes?
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