Northeastern WOOTers Mock AIME I Problems/Problem 7

Problem 7

Find the value of $\sum_{n=0}^{100}\left\lfloor\frac{3n+4}{13}\right\rfloor-\left\lfloor\frac{n-28+\left\lfloor\frac{n-7}{13}\right\rfloor}{4}\right\rfloor.$

Solution

As of now,

$\sum_{n=0}^{100}\left\lfloor\frac{3n+4}{13}\right\rfloor = 1150$ $\sum_{n=0}^{100}\left\lfloor\frac{n-28+\left\lfloor\frac{n-7}{13}\right\rfloor}{4}\right\rfloor = 588$

Giving an answer of 562.

(Thread: https://artofproblemsolving.com/community/c5h2020524_floor_function_problem_mock_aime)

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Northeastern WOOTers Mock AIME I Problems/Problem 7

Problem 7

Solution