{"status": "success", "data": {"description_md": "Let $n \\ge m \\ge 2$ be integers, and consider an $m \\times n$ grid of unit squares. Such grids will contain many rectangles whose vertices are points on the grid, and whose edges are lines from the grid. Find the sum of all distinct values of $m+n$ such that the $m \\times n$ grid contains exactly $100$ non-congruent rectangles.", "description_html": "<p>Let <span class=\"katex--inline\">n \\ge m \\ge 2</span> be integers, and consider an <span class=\"katex--inline\">m \\times n</span> grid of unit squares. Such grids will contain many rectangles whose vertices are points on the grid, and whose edges are lines from the grid. Find the sum of all distinct values of <span class=\"katex--inline\">m+n</span> such that the <span class=\"katex--inline\">m \\times n</span> grid contains exactly <span class=\"katex--inline\">100</span> non-congruent rectangles.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "Christmas Contest - Individual Round - Problem 16", "can_next": true, "can_prev": true, "nxt": "/problem/christmas1_individual-p17", "prev": "/problem/christmas1_individual-p15"}}