AMC / AIME · Stars and Bars · Easy

Stars and Bars: How many ordered pairs of positive integers have sum math?

Integer solutions to linear equations.

Try the problem

How many ordered pairs of **positive** integers have sum 1515?

Hint and answer

Concept to use

Nonnegative: $\binom{n+k-1}{k-1}$.

Hint

(1,14),(2,13),…(1,14),(2,13),\ldots.

Answer

14

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