{"status": "success", "data": {"description_md": "There are $24$ students numbered $1,2, ... ,24$ such that student $i$ is only friends with students $2i$ and $2i+1$. Alex wishes to distribute toys to the students but he only has five different choices for the color of the toy.\n\nIf $N$ is the number of ways he can distribute the toys such that every pair of friends must have a different color toy, find the number of factors of $N$.", "description_html": "<p>There are <span class=\"katex--inline\">24</span> students numbered <span class=\"katex--inline\">1,2, ... ,24</span> such that student <span class=\"katex--inline\">i</span> is only friends with students <span class=\"katex--inline\">2i</span> and <span class=\"katex--inline\">2i+1</span>. Alex wishes to distribute toys to the students but he only has five different choices for the color of the toy.</p>&#10;<p>If <span class=\"katex--inline\">N</span> is the number of ways he can distribute the toys such that every pair of friends must have a different color toy, find the number of factors of <span class=\"katex--inline\">N</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "Christmas Contest - Team Round - Problem 23", "can_next": true, "can_prev": true, "nxt": "/problem/christmas1_team-p24", "prev": "/problem/christmas1_team-p22"}}