{"status": "success", "data": {"description_md": "One commercially available ten-button lock may be opened by depressing -- in any order -- the correct five buttons. The sample shown below has $\\{1, 2, 3, 6, 9\\}$ as its combination. Suppose that these locks are redesigned so that sets of as many as nine buttons or as few as one button could serve as combinations. How many additional combinations would this allow?<br><br>$\\includegraphics[width=126, height=89, totalheight=89]{https://latex.artofproblemsolving.com/9/6/3/9639addd82f5f37b0a5ae85a8aad874cb4e081f0.png}$\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>One commercially available ten-button lock may be opened by depressing &#8211; in any order &#8211; the correct five buttons. The sample shown below has <span class=\"katex--inline\">\\{1, 2, 3, 6, 9\\}</span> as its combination. Suppose that these locks are redesigned so that sets of as many as nine buttons or as few as one button could serve as combinations. How many additional combinations would this allow?<br/><br/><img src=\"https://latex.artofproblemsolving.com/9/6/3/9639addd82f5f37b0a5ae85a8aad874cb4e081f0.png\" width=\"126\" height=\"89\" class=\"problem-image\"/></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": "1988 AIME Problem 1", "can_next": true, "can_prev": false, "nxt": "/problem/88_aime_p02", "prev": ""}}