{"status": "success", "data": {"description_md": "In a room, there are $5$ light bulbs turned off, each paired up with a button. At the end of every minute, Alice presses a button and turns the corresponding light bulb on. The button can be pressed even if the light is currently on. If $n$ is the total number of times a button was pressed, the corresponding light bulb will inexplicably switch back off $n^2$ minutes after the latest button press. Following optimal strategy, what is the minimum amount of time (in minutes) until Alice is able to turn on all lights, even if just for a moment?", "description_html": "<p>In a room, there are <span class=\"katex--inline\">5</span> light bulbs turned off, each paired up with a button. At the end of every minute, Alice presses a button and turns the corresponding light bulb on. The button can be pressed even if the light is currently on. If <span class=\"katex--inline\">n</span> is the total number of times a button was pressed, the corresponding light bulb will inexplicably switch back off <span class=\"katex--inline\">n^2</span> minutes after the latest button press. Following optimal strategy, what is the minimum amount of time (in minutes) until Alice is able to turn on all lights, even if just for a moment?</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 6, "problem_name": "TxO Math Bowl 2024 - Team Contest - Problem 21", "can_next": true, "can_prev": true, "nxt": "/problem/txo2024team-p22", "prev": "/problem/txo2024team-p20"}}