{"status": "success", "data": {"description_md": "**POTD July 16, 2024**\n\nDefine the following function $$\\large{f(x, y) = \\sum\\limits_{n=0}^{\\left\\lfloor\\log_2{\\max(x,y)}\\right\\rfloor}2^n\\left[\\left(\\left\\lfloor\\dfrac{x}{2^n}\\right\\rfloor+\\left\\lfloor\\dfrac{y}{2^n}\\right\\rfloor\\right)\\text{mod }2\\right]}. $$ Find $$\\large{f(1, f(2, f(3, f(4, \\ldots f(99, 100))\\ldots))))} $$", "description_html": "<p><strong>POTD July 16, 2024</strong></p>&#10;<p>Define the following function <span class=\"katex--display\">\\large{f(x, y) = \\sum\\limits_{n=0}^{\\left\\lfloor\\log_2{\\max(x,y)}\\right\\rfloor}2^n\\left[\\left(\\left\\lfloor\\dfrac{x}{2^n}\\right\\rfloor+\\left\\lfloor\\dfrac{y}{2^n}\\right\\rfloor\\right)\\text{mod }2\\right]}.</span> Find <span class=\"katex--display\">\\large{f(1, f(2, f(3, f(4, \\ldots f(99, 100))\\ldots))))}</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 6, "problem_name": "Problem of the Day #219", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}