{"status": "success", "data": {"description_md": "Alex and Alvin are playing a game with $N$ slots. Every turn, Alex can either place $1$ coin in $2$ slots, or $2$ coins in $1$ slot. Then, Alvin can remove all the coins from $1$ slot. What is the minimum $N$ such that no matter what Alvin does, Alex can form a stack of $10$ coins in $1$ slot at some point in time?", "description_html": "<p>Alex and Alvin are playing a game with <span class=\"katex--inline\">N</span> slots. Every turn, Alex can either place <span class=\"katex--inline\">1</span> coin in <span class=\"katex--inline\">2</span> slots, or <span class=\"katex--inline\">2</span> coins in <span class=\"katex--inline\">1</span> slot. Then, Alvin can remove all the coins from <span class=\"katex--inline\">1</span> slot. What is the minimum <span class=\"katex--inline\">N</span> such that no matter what Alvin does, Alex can form a stack of <span class=\"katex--inline\">10</span> coins in <span class=\"katex--inline\">1</span> slot at some point in time?</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "AMC Practice #1 - Problem 8", "can_next": true, "can_prev": true, "nxt": "/problem/amc1-p09", "prev": "/problem/amc1-p07"}}