{"status": "success", "data": {"description_md": "The figures $F_1$, $F_2$, $F_3$, and $F_4$ shown are the first in a sequence of figures. For $n\\ge3$, $F_n$ is constructed from $F_{n - 1}$ by surrounding it with a square and placing one more diamond on each side of the new square than $F_{n - 1}$ had on each side of its outside square. For example, figure $F_3$ has $13$ diamonds. How many diamonds are there in figure $F_{20}$?\n$$\n
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$$\n\n$\\mathrm{(A)}\\ 401\n\\qquad\n\\mathrm{(B)}\\ 485\n\\qquad\n\\mathrm{(C)}\\ 585\n\\qquad\n\\mathrm{(D)}\\ 626\n\\qquad\n\\mathrm{(E)}\\ 761$", "description_html": "

The figures F_1 , F_2 , F_3 , and F_4 shown are the first in a sequence of figures. For n\\ge3 , F_n is constructed from F_{n - 1} by surrounding it with a square and placing one more diamond on each side of the new square than F_{n - 1} had on each side of its outside square. For example, figure F_3 has 13 diamonds. How many diamonds are there in figure F_{20} ?
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\\mathrm{(A)}\\ 401\n\\qquad\n\\mathrm{(B)}\\ 485\n\\qquad\n\\mathrm{(C)}\\ 585\n\\qquad\n\\mathrm{(D)}\\ 626\n\\qquad\n\\mathrm{(E)}\\ 761

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Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2009 AMC 10A Problem 15", "can_next": true, "can_prev": true, "nxt": "/problem/09_amc10A_p16", "prev": "/problem/09_amc10A_p14"}}