{"status": "success", "data": {"description_md": "**POTD May 20, 2024**\n\nLet $n > 1$ be an odd integer. On an $n \\times n$ chessboard the center square and four corners are deleted. We wish to group the remaining $n^2 - 5$ squares into  $\\frac{1}{2}(n^2 - 5)$ pairs, such that the two squares in each pair intersect at exactly one point (i.e. they are diagonally adjacent, sharing a single corner). Find the sum of the odd integers $n > 1$ for which this is possible.\n\nTry to prove this question as well!", "description_html": "<p><strong>POTD May 20, 2024</strong></p>&#10;<p>Let <span class=\"katex--inline\">n &gt; 1</span> be an odd integer. On an <span class=\"katex--inline\">n \\times n</span> chessboard the center square and four corners are deleted. We wish to group the remaining <span class=\"katex--inline\">n^2 - 5</span> squares into  <span class=\"katex--inline\">\\frac{1}{2}(n^2 - 5)</span> pairs, such that the two squares in each pair intersect at exactly one point (i.e. they are diagonally adjacent, sharing a single corner). Find the sum of the odd integers <span class=\"katex--inline\">n &gt; 1</span> for which this is possible.</p>&#10;<p>Try to prove this question as well!</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "Problem of the Day #162", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}