{"status": "success", "data": {"description_md": "In the sequence of fractions $\\frac{1}{1}, \\frac{2}{1}, \\frac{1}{2}, \\frac{3}{1}, \\frac{2}{2}, \\frac{1}{3}, \\frac{4}{1}, \\frac{3}{2}, \\frac{2}{3}, \\frac{1}{4}, \\frac{5}{1}, \\ldots$, fractions equivalent to any given fraction occur many times. For example, fractions equivalent to $\\frac{1}{2}$ occur for the first two times in positions 3 and 14. In which position is the fifth occurrence of a fraction equivalent to $\\frac{3}{7}$?\n\n$\\text{(A)}\\ 1207\\qquad\\text{(B)}\\ 1208\\qquad\\text{(C)}\\ 1209\\qquad\\text{(D)}\\ 1210\\qquad\\text{(E)}\\ 1211$\n\n___\n\n**[Pascal](https://www.cemc.uwaterloo.ca/contests/past_contests.html#pcf), by [CEMC](https://cemc.uwaterloo.ca/), is licensed under the [CC BY-NC 3.0 DEED](https://creativecommons.org/licenses/by-nc/3.0/). They are not affiliated with or endorse TopsOJ in any way.**\n", "description_html": "

In the sequence of fractions \\frac{1}{1}, \\frac{2}{1}, \\frac{1}{2}, \\frac{3}{1}, \\frac{2}{2}, \\frac{1}{3}, \\frac{4}{1}, \\frac{3}{2}, \\frac{2}{3}, \\frac{1}{4}, \\frac{5}{1}, \\ldots, fractions equivalent to any given fraction occur many times. For example, fractions equivalent to \\frac{1}{2} occur for the first two times in positions 3 and 14. In which position is the fifth occurrence of a fraction equivalent to \\frac{3}{7}?

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\\text{(A)}\\ 1207\\qquad\\text{(B)}\\ 1208\\qquad\\text{(C)}\\ 1209\\qquad\\text{(D)}\\ 1210\\qquad\\text{(E)}\\ 1211

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Pascal, by CEMC, is licensed under the CC BY-NC 3.0 DEED. They are not affiliated with or endorse TopsOJ in any way.

\n", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2004 Pascal Problem 24", "can_next": true, "can_prev": true, "nxt": "/problem/04_pascal_p25", "prev": "/problem/04_pascal_p23"}}