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You are a math expert with clear and concise reasoning. Solve this problem step-by-step and box your final numerical answer:
A printed document with 55 pages is renumbered in reverse order. If page 1 becomes 55, and so on, what number does the original page 26 become?
## Step 1: Identify the transformation
Each page \( n \) is renumbered in reverse as \( 56 - n \).
## Step 2: Compute the new number of the original page
The original page is 26, so the new number is:
\[
56 - 26 = 30
\]
## Step 3: Provide the final answer
The final answer is: \( \boxed{30} \) |
You are a math expert with clear and concise reasoning. Solve this problem step-by-step and box your final numerical answer:
There are 60 pages in a manual, numbered sequentially from 1 to 60. If they are re-labeled in reverse order (so that page 1 becomes 60, page 2 becomes 59, etc.), what is the new number of page 18?
## Step 1: Identify the transformation
Each page \( n \) is renumbered in reverse as \( 61 - n \).
## Step 2: Compute the new number of the original page
The original page is 18, so the new number is:
\[
61 - 18 = 43
\]
## Step 3: Provide the final answer
The final answer is: \( \boxed{43} \) |
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: \( \boxed{36} \) |
You are a math expert with clear and concise reasoning. Solve this problem step-by-step and box your final numerical answer:
A notebook contains 40 pages, labeled from 1 to 40. The pages are renumbered in reverse (page 1 becomes 40, page 2 becomes 39, etc.). What does page 15 become?
## Step 1: Identify the transformation
Each page \( n \) is renumbered in reverse as \( 41 - n \).
## Step 2: Compute the new number of the original page
The original page is 15, so the new number is:
\[
41 - 15 = 26
\]
## Step 3: Provide the final answer
The final answer is: \( \boxed{26} \) |
You are a math expert with clear and concise reasoning. Solve this problem step-by-step and box your final numerical answer:
You have a thesis with 35 pages, originally labeled 1 to 35. It's renumbered in reverse (1 becomes 35, 2 becomes 34, and so on). What does page 20 become?
## Step 1: Identify the transformation
Each page \( n \) is renumbered in reverse as \( 36 - n \).
## Step 2: Compute the new number of the original page
The original page is 20, so the new number is:
\[
36 - 20 = 16
\]
## Step 3: Provide the final answer
The final answer is: \( \boxed{16} \) |
You are a math expert with clear and concise reasoning. Solve this problem step-by-step and box your final numerical answer:
Consider a journal with 25 pages, numbered 1 through 25. If renumbered in reverse (page 1 becomes 25, page 2 becomes 24, etc.), what page number will the original page 9 have?
## Step 1: Identify the transformation
Each page \( n \) is renumbered in reverse as \( 26 - n \).
## Step 2: Compute the new number of the original page
The original page is 9, so the new number is:
\[
26 - 9 = 17
\]
## Step 3: Provide the final answer
The final answer is: \( \boxed{17} \) |
You are a math expert with clear and concise reasoning. Solve this problem step-by-step and box your final numerical answer:
An album of 70 pages is renumbered in reverse, with page 1 becoming 70, page 2 becoming 69, and so on. What number does page 33 become?
## Step 1: Identify the transformation
Each page \( n \) is renumbered in reverse as \( 71 - n \).
## Step 2: Compute the new number of the original page
The original page is 33, so the new number is:
\[
71 - 33 = 38
\]
## Step 3: Provide the final answer
The final answer is: \( \boxed{38} \) |
You are a math expert with clear and concise reasoning. Solve this problem step-by-step and box your final numerical answer:
A comic book has 30 pages, labeled 1 to 30. If every page is re-numbered in reverse (1 becomes 30, 2 becomes 29, etc.), what number does page 12 turn into?
## Step 1: Identify the transformation
Each page \( n \) is renumbered in reverse as \( 31 - n \).
## Step 2: Compute the new number of the original page
The original page is 12, so the new number is:
\[
31 - 12 = 19
\]
## Step 3: Provide the final answer
The final answer is: \( \boxed{19} \) |
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