{"status": "success", "data": {"description_md": "Jerrily is a dot on a $2$ dimensional plane. On his first move, Jerrily moves forwards $1$ unit and makes a $45^{\\circ}$ turn, on his second move, Jerrily moves forward $2$ units and makes a $45^{\\circ}$ turn. This pattern continues where, every move, Jerrily moves forward 1 more step than his last move, and makes a turn of $45^{\\circ}$. If Jerrily is facing an arbitrary direction, after $2024$ moves, the distance Jerrily traveled from the starting point can be represented as $m\\sqrt{n} \\cdot (\\sqrt{2 +\\sqrt2})$. What is the sum of the digits of the value of $m + n$?", "description_html": "<p>Jerrily is a dot on a <span class=\"katex--inline\">2</span> dimensional plane. On his first move, Jerrily moves forwards <span class=\"katex--inline\">1</span> unit and makes a <span class=\"katex--inline\">45^{\\circ}</span> turn, on his second move, Jerrily moves forward <span class=\"katex--inline\">2</span> units and makes a <span class=\"katex--inline\">45^{\\circ}</span> turn. This pattern continues where, every move, Jerrily moves forward 1 more step than his last move, and makes a turn of <span class=\"katex--inline\">45^{\\circ}</span>. If Jerrily is facing an arbitrary direction, after <span class=\"katex--inline\">2024</span> moves, the distance Jerrily traveled from the starting point can be represented as <span class=\"katex--inline\">m\\sqrt{n} \\cdot (\\sqrt{2 +\\sqrt2})</span>. What is the sum of the digits of the value of <span class=\"katex--inline\">m + n</span>?</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "Christmas Contest - Guts Round - Set 5 Problem 1", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}