Brute Force?

Algebra Level 3

$\large \left \lceil \lfloor \pi \rfloor + \left\lfloor \pi + \dfrac{1}{6}\right \rfloor + \left \lfloor \pi + \dfrac{2}{6} \right \rfloor + \left \lfloor \pi + \dfrac{3}{6} \right \rfloor + \left \lfloor \pi + \dfrac{4}{6}\right \rfloor +\left \lfloor \pi + \dfrac{5}{6}\right \rfloor \right \rceil + 1 = \, ?$

Notations : $\lfloor \cdot \rfloor$ denotes the floor function and $\lceil \cdot \rceil$ denotes the ceiling function .

Too easy? Try this .

The answer is 19.

1 solution

Ralph Macarasig
Aug 6, 2016

Using brute force, we know that the approximate value of $\pi$ is $3.142$ to three decimal places. Then, the approximate value of $\frac{5}{6}$ is $0.833$ to 3 decimal places. Hence, the approximate value of $\pi + \frac{5}{6}$ is $3.975$ which is less than $4$ . Therefore,

$\lceil \lfloor \pi \rfloor + \lfloor \pi + \frac{1}{6}\rfloor + \lfloor \pi + \frac{2}{6}\rfloor +\lfloor \pi + \frac{3}{6}\rfloor + \lfloor \pi + \frac{4}{6}\rfloor + \lfloor \pi + \frac{5}{6}\rfloor \rceil + 1$

$= \lceil 3 + 3 + 3 + 3 + 3 + 3\rceil + 1$

$= \boxed{19}$

Brute Force?

Too easy? Try this .

The answer is 19.

1 solution

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