{"status": "success", "data": {"description_md": "In Pascal's Triangle, each entry is the sum of the two entries above it. The first few rows of the triangle are shown below.

\n$$\\begin{array}{c@{\\hspace{8em}}
c@{\\hspace{6pt}}c@{\\hspace{6pt}}c@{\\hspace{6pt}}c@{\\hspace{4pt}}c@{\\hspace{2pt}}
c@{\\hspace{2pt}}c@{\\hspace{2pt}}c@{\\hspace{2pt}}c@{\\hspace{3pt}}c@{\\hspace{6pt}}
c@{\\hspace{6pt}}c@{\\hspace{6pt}}c} \\vspace{4pt}
\\text{Row 0: } & & & & & & & 1 & & & & & & \\\\\\vspace{4pt}
\\text{Row 1: } & & & & & & 1 & & 1 & & & & & \\\\\\vspace{4pt}
\\text{Row 2: } & & & & & 1 & & 2 & & 1 & & & & \\\\\\vspace{4pt}
\\text{Row 3: } & & & & 1 & & 3 & & 3 & & 1 & & & \\\\\\vspace{4pt}
\\text{Row 4: } & & & 1 & & 4 & & 6 & & 4 & & 1 & & \\\\\\vspace{4pt}
\\text{Row 5: } & & 1 & & 5 & &10& &10 & & 5 & & 1 & \\\\\\vspace{4pt}
\\text{Row 6: } & 1 & & 6 & &15& &20& &15 & & 6 & & 1
\\end{array} $$ In which row of Pascal's Triangle do three consecutive entries occur that are in the ratio $3: 4: 5$?\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "

In Pascal’s Triangle, each entry is the sum of the two entries above it. The first few rows of the triangle are shown below.

\\begin{array}{c@{\\hspace{8em}}<br>c@{\\hspace{6pt}}c@{\\hspace{6pt}}c@{\\hspace{6pt}}c@{\\hspace{4pt}}c@{\\hspace{2pt}}<br>c@{\\hspace{2pt}}c@{\\hspace{2pt}}c@{\\hspace{2pt}}c@{\\hspace{3pt}}c@{\\hspace{6pt}}<br>c@{\\hspace{6pt}}c@{\\hspace{6pt}}c} \\vspace{4pt}<br>\\text{Row 0: } & & & & & & & 1 & & & & & & \\\\\\vspace{4pt}<br>\\text{Row 1: } & & & & & & 1 & & 1 & & & & & \\\\\\vspace{4pt}<br>\\text{Row 2: } & & & & & 1 & & 2 & & 1 & & & & \\\\\\vspace{4pt}<br>\\text{Row 3: } & & & & 1 & & 3 & & 3 & & 1 & & & \\\\\\vspace{4pt}<br>\\text{Row 4: } & & & 1 & & 4 & & 6 & & 4 & & 1 & & \\\\\\vspace{4pt}<br>\\text{Row 5: } & & 1 & & 5 & &10& &10 & & 5 & & 1 & \\\\\\vspace{4pt}<br>\\text{Row 6: } & 1 & & 6 & &15& &20& &15 & & 6 & & 1<br>\\end{array}
In which row of Pascal’s Triangle do three consecutive entries occur that are in the ratio 3: 4: 5?

Leading zeroes must be inputted, so if your answer is 34, then input 034. 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": "1992 AIME Problem 4", "can_next": true, "can_prev": true, "nxt": "/problem/92_aime_p05", "prev": "/problem/92_aime_p03"}}