{"status": "success", "data": {"description_md": "A set of tiles numbered $1$ through $100$ is modified repeatedly by the following operation: remove all tiles numbered with a perfect square, and renumber the remaining tiles consecutively starting with $1$. How many times must the operation be performed to reduce the number of tiles in the set to one?\n\n$\\text{(A)}\\ 10 \\qquad \\text{(B)}\\ 11 \\qquad \\text{(C)}\\ 18 \\qquad \\text{(D)}\\ 19 \\qquad \\text{(E)}\\ 20$", "description_html": "<p>A set of tiles numbered <span class=\"katex--inline\">1</span> through <span class=\"katex--inline\">100</span> is modified repeatedly by the following operation: remove all tiles numbered with a perfect square, and renumber the remaining tiles consecutively starting with <span class=\"katex--inline\">1</span>. How many times must the operation be performed to reduce the number of tiles in the set to one?</p>&#10;<p><span class=\"katex--inline\">\\text{(A)}\\ 10 \\qquad \\text{(B)}\\ 11 \\qquad \\text{(C)}\\ 18 \\qquad \\text{(D)}\\ 19 \\qquad \\text{(E)}\\ 20</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "2002 AMC 10A Problem 22", "can_next": true, "can_prev": true, "nxt": "/problem/02_amc10A_p23", "prev": "/problem/02_amc10A_p21"}}