{"status": "success", "data": {"description_md": "Let $a$, $b$, and $c$ be digits with $a\\ne 0$. The three-digit integer $abc$ lies one third of the way from the square of a positive integer to the square of the next larger integer. The integer $acb$ lies two thirds of the way between the same two squares. What is $a+b+c$?\n\n$\\mathrm {(A)} 10\\qquad \\mathrm {(B)} 13\\qquad \\mathrm {(C)} 16\\qquad \\mathrm {(D)} 18\\qquad \\mathrm {(E)} 21$\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>Let  <span class=\"katex--inline\">a</span> ,  <span class=\"katex--inline\">b</span> , and  <span class=\"katex--inline\">c</span>  be digits with  <span class=\"katex--inline\">a\\ne 0</span> . The three-digit integer  <span class=\"katex--inline\">abc</span>  lies one third of the way from the square of a positive integer to the square of the next larger integer. The integer  <span class=\"katex--inline\">acb</span>  lies two thirds of the way between the same two squares. What is  <span class=\"katex--inline\">a+b+c</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\mathrm {(A)} 10\\qquad \\mathrm {(B)} 13\\qquad \\mathrm {(C)} 16\\qquad \\mathrm {(D)} 18\\qquad \\mathrm {(E)} 21</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": 3, "problem_name": "2007 AMC 12B Problem 18", "can_next": true, "can_prev": true, "nxt": "/problem/07_amc12B_p19", "prev": "/problem/07_amc12B_p17"}}