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Omni-MATH / The number 3003 is the only number known to appear eight times in Pascal's…

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problem

The number 3003 is the only number known to appear eight times in Pascal's triangle, at positions $\binom{3003}{1},\binom{3003}{3002},\binom{a}{2},\binom{a}{a-2},\binom{15}{b},\binom{15}{15-b},\binom{14}{6},\binom{14}{8}$. Compute a+b(15−b)a+b(15-b).
Plain-text mathematical notation (without MathML)
The number 3003 is the only number known to appear eight times in Pascal's triangle, at positions $\binom{3003}{1},\binom{3003}{3002},\binom{a}{2},\binom{a}{a-2},\binom{15}{b},\binom{15}{15-b},\binom{14}{6},\binom{14}{8}$. Compute a+b(15−b).
Original LaTeX notation
The number 3003 is the only number known to appear eight times in Pascal's triangle, at positions $\binom{3003}{1},\binom{3003}{3002},\binom{a}{2},\binom{a}{a-2},\binom{15}{b},\binom{15}{15-b},\binom{14}{6},\binom{14}{8}$. Compute $a+b(15-b)$.

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Source and history

task_id
1d7c8403-db88-5d4a-9e9f-e11a05203a61
task_key
test--1d7c8403-db88-5d4a-9e9f-e11a05203a61
task_revision_id
1
config / split
/ test

Official source

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