{"status": "success", "data": {"description_md": "Find the number of permutations $x_1, x_2, x_3, x_4, x_5$ of numbers $1, 2, 3, 4, 5$ such that the sum of five products<br>\n$$x_1x_2x_3 + x_2x_3x_4 + x_3x_4x_5 + x_4x_5x_1 + x_5x_1x_2 $$is divisible by $3$.\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full 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>Find the number of permutations <span class=\"katex--inline\">x_1, x_2, x_3, x_4, x_5</span> of numbers <span class=\"katex--inline\">1, 2, 3, 4, 5</span> such that the sum of five products<br/><span class=\"katex--display\">x_1x_2x_3 + x_2x_3x_4 + x_3x_4x_5 + x_4x_5x_1 + x_5x_1x_2</span>is divisible by <span class=\"katex--inline\">3</span>.</p>&#10;<hr><p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. 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": "2021 AIME II Problem 3", "can_next": true, "can_prev": true, "nxt": "/problem/21_aime_II_p04", "prev": "/problem/21_aime_II_p02"}}