{"status": "success", "data": {"description_md": "The first $2007$ positive integers are each written in base $3$. How many of these base-$3$ representations are palindromes? (A palindrome is a number that reads the same forward and backward.)\n\n$\\mathrm {(A)} 100\\qquad \\mathrm {(B)} 101\\qquad \\mathrm {(C)} 102\\qquad \\mathrm {(D)} 103\\qquad \\mathrm {(E)} 104$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>The first  <span class=\"katex--inline\">2007</span>  positive integers are each written in base  <span class=\"katex--inline\">3</span> . How many of these base- <span class=\"katex--inline\">3</span>  representations are palindromes? (A palindrome is a number that reads the same forward and backward.)</p>&#10;<p> <span class=\"katex--inline\">\\mathrm {(A)} 100\\qquad \\mathrm {(B)} 101\\qquad \\mathrm {(C)} 102\\qquad \\mathrm {(D)} 103\\qquad \\mathrm {(E)} 104</span> </p>&#10;<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2007 AMC 12B Problem 21", "can_next": true, "can_prev": true, "nxt": "/problem/07_amc12B_p22", "prev": "/problem/07_amc12B_p20"}}