{"status": "success", "data": {"description_md": "*This is a user suggested problem. The TopsOJ staff thanks and gives full credit to [vsarca](https://www.topsoj.com/users/vsarca/profile) for their contribution.*\n\n****\n\nI am making stuffed animals from bodies, heads, and tails. I can only operate on one animal body at a time, and I may not operate on another animal body until I finish my current animal. I create animals by flipping a coin; when the coin flips heads, I add a head if my current animal does not already have a head, and when it flips tails, I add a tail if my current animal does not already have a tail. An animal is completed once it has a head and a tail, at which point I set it aside and begin another one.\n\nIf my expected number of completed animals after $40$ coin flips is $\\frac{p}{q}$, where $\\gcd(p,q)=1$, find $p+q$.\n\n****\n\nNote: it is **STRONGLY RECOMMENDED** by the problem author to find the closed form first, as this was the original problem statement, **and to use a calculator to compute the final answer. The required number of coin flips is 40 to prevent users from cheesing this problem with Python.**", "description_html": "<p><em>This is a user suggested problem. The TopsOJ staff thanks and gives full credit to <a href=\"https://www.topsoj.com/users/vsarca/profile\">vsarca</a> for their contribution.</em></p>&#10;<hr/>&#10;<p>I am making stuffed animals from bodies, heads, and tails. I can only operate on one animal body at a time, and I may not operate on another animal body until I finish my current animal. I create animals by flipping a coin; when the coin flips heads, I add a head if my current animal does not already have a head, and when it flips tails, I add a tail if my current animal does not already have a tail. An animal is completed once it has a head and a tail, at which point I set it aside and begin another one.</p>&#10;<p>If my expected number of completed animals after <span class=\"katex--inline\">40</span> coin flips is <span class=\"katex--inline\">\\frac{p}{q}</span>, where <span class=\"katex--inline\">\\gcd(p,q)=1</span>, find <span class=\"katex--inline\">p+q</span>.</p>&#10;<hr/>&#10;<p>Note: it is <strong>STRONGLY RECOMMENDED</strong> by the problem author to find the closed form first, as this was the original problem statement, <strong>and to use a calculator to compute the final answer. The required number of coin flips is 40 to prevent users from cheesing this problem with Python.</strong></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "Stuffed Animals", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}