{"status": "success", "data": {"description_md": "Harold, Tanya, and Ulysses paint a very long picket fence. Harold starts with the first picket and paints every $h$th picket; Tanya starts with the second picket and paints every $t$th picket; and Ulysses starts with the third picket and paints every $u$th picket. Call the positive integer $100h + 10t + u$ $paintable$ when the triple $(h,t, u)$ of positive integers results in every picket being painted exactly once. Find the sum of all the paintable integers.\n\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`\n\n___\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>Harold, Tanya, and Ulysses paint a very long picket fence. Harold starts with the first picket and paints every <span class=\"katex--inline\">h</span>th picket; Tanya starts with the second picket and paints every <span class=\"katex--inline\">t</span>th picket; and Ulysses starts with the third picket and paints every <span class=\"katex--inline\">u</span>th picket. Call the positive integer <span class=\"katex--inline\">100h + 10t + u</span> <span class=\"katex--inline\">paintable</span> when the triple <span class=\"katex--inline\">(h,t, u)</span> of positive integers results in every picket being painted exactly once. Find the sum of all the paintable integers.</p>&#10;<p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code></p>&#10;<hr/>&#10;<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>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "2002 AIME I Problem 9", "can_next": true, "can_prev": true, "nxt": "/problem/02_aime_I_p10", "prev": "/problem/02_aime_I_p08"}}