text: You are a math expert with clear and concise reasoning. Solve this problem step-by-step and box your final numerical answer:
  A book contains 80 pages, from 1 to 80. The pages are renumbered backward (page 1 becomes 80, page 2 becomes 79, and so on). What will be the number of page 45 after renumbering?
  ## Step 1: Identify the transformation
  Each page \( n \) is renumbered in reverse as \( 81 - n \).
  
  ## Step 2: Compute the new number of the original page
  The original page is 45, so the new number is:
  \[
  81 - 45 = 36
  \]
  
  ## Step 3: Provide the final answer
  The final answer is: \( \boxed{36} \)