{"status": "success", "data": {"description_md": "Suppose there is a sequence of numbers $S = \\{a_1, a_2, a_3, \\cdots, a_n\\}$. Define $\\Delta S = \\{a_2-a_1,\\;a_3-a_2,\\;\\ldots,\\;a_n-a_{n-1}\\}$. If all elements of $\\Delta(\\Delta(\\Delta S)) = 1$ and $a_4=a_9=a_{96}=0$, find $|a_1|$.", "description_html": "<p>Suppose there is a sequence of numbers <span class=\"katex--inline\">S = \\{a_1, a_2, a_3, \\cdots, a_n\\}</span>. Define <span class=\"katex--inline\">\\Delta S = \\{a_2-a_1,\\;a_3-a_2,\\;\\ldots,\\;a_n-a_{n-1}\\}</span>. If all elements of <span class=\"katex--inline\">\\Delta(\\Delta(\\Delta S)) = 1</span> and <span class=\"katex--inline\">a_4=a_9=a_{96}=0</span>, find <span class=\"katex--inline\">|a_1|</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 7, "problem_name": "TxO Math Bowl 2024 - Team Contest - Problem 30", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/txo2024team-p29"}}