Difference between revisions of "Northeastern WOOTers Mock AIME I Problems/Problem 7"

(Solution)
(Solution)
 
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<cmath>\sum_{n=0}^{100}\left\lfloor\frac{n-28+\left\lfloor\frac{n-7}{13}\right\rfloor}{4}\right\rfloor = 588</cmath>
 
<cmath>\sum_{n=0}^{100}\left\lfloor\frac{n-28+\left\lfloor\frac{n-7}{13}\right\rfloor}{4}\right\rfloor = 588</cmath>
  
Giving an answer of 662.
+
Giving an answer of 562.
  
  
 
(Thread: https://artofproblemsolving.com/community/c5h2020524_floor_function_problem_mock_aime)
 
(Thread: https://artofproblemsolving.com/community/c5h2020524_floor_function_problem_mock_aime)

Latest revision as of 22:52, 2 March 2020

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)