{"status": "success", "data": {"description_md": "In a rectangular array of points, with 5 rows and $N$ columns, the points are numbered consecutively from left to right beginning with the top row. Thus the top row is numbered 1 through $N,$ the second row is numbered $N+1$ through $2N,$ and so forth. Five points, $P_1, P_2, P_3, P_4,$ and $P_5,$ are selected so that each $P_i$ is in row $i.$ Let $x_i$ be the number associated with $P_i.$ Now renumber the array consecutively from top to bottom, beginning with the first column. Let $y_i$ be the number associated with $P_i$ after the renumbering. It is found that $x_1=y_2,$ $x_2=y_1,$ $x_3=y_4,$ $x_4=y_5,$ and $x_5=y_3.$ Find the smallest possible value of $N.$\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>In a rectangular array of points, with 5 rows and <span class=\"katex--inline\">N</span> columns, the points are numbered consecutively from left to right beginning with the top row. Thus the top row is numbered 1 through <span class=\"katex--inline\">N,</span> the second row is numbered <span class=\"katex--inline\">N+1</span> through <span class=\"katex--inline\">2N,</span> and so forth. Five points, <span class=\"katex--inline\">P_1, P_2, P_3, P_4,</span> and <span class=\"katex--inline\">P_5,</span> are selected so that each <span class=\"katex--inline\">P_i</span> is in row <span class=\"katex--inline\">i.</span> Let <span class=\"katex--inline\">x_i</span> be the number associated with <span class=\"katex--inline\">P_i.</span> Now renumber the array consecutively from top to bottom, beginning with the first column. Let <span class=\"katex--inline\">y_i</span> be the number associated with <span class=\"katex--inline\">P_i</span> after the renumbering. It is found that <span class=\"katex--inline\">x_1=y_2,</span> <span class=\"katex--inline\">x_2=y_1,</span> <span class=\"katex--inline\">x_3=y_4,</span> <span class=\"katex--inline\">x_4=y_5,</span> and <span class=\"katex--inline\">x_5=y_3.</span> Find the smallest possible value of <span class=\"katex--inline\">N.</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": 5, "problem_name": "2001 AIME I Problem 11", "can_next": true, "can_prev": true, "nxt": "/problem/01_aime_I_p12", "prev": "/problem/01_aime_I_p10"}}