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[ { "content": "You are a math expert with clear and concise reasoning. Solve this problem step-by-step and box your final numerical answer:", "role": "system" }, { "content": "A book with 50 pages, numbered 1 to 50, has its pages renumbered in reverse (page 1 becomes 50, page 2 becomes 49, etc.). How...
[ { "content": "Those pages will have the same ones digit in both positions.\n\n## Step 1: Understand the problem\nWe have a book with 50 pages, initially numbered 1 to 50. The pages are then renumbered in reverse. We need to find how many pages retain the same ones digit before and after renumbering.\n\n## Step ...
[ { "content": "The ones digits that retain the same value are 1, 2, 3, 4, 5, and 6.\n\n## Step 1: Understand the problem and the given conditions\nThe problem asks us to find how many pages retain the same ones digit before and after renumbering, where the pages are numbered from 1 to 50.\n\n## Step 2: Analyze t...
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