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Floor and Ceiling Functions

Floor functions map a real number x to the largest integer less than or equal to x. You can probably guess what the ceiling function does.

Floor and Ceiling Functions: Level 3 Challenges


\[ \large {\lfloor -3.2 \rfloor =\, ? } \]

Given that \(x\) is a real number but not an integer, compute \( \lfloor x \rfloor + \lfloor - x \rfloor \).

\[\left\lfloor \left| \frac{2x-3}{4} \right| \right\rfloor = 5\]

What is the largest negative integer \(x\) that satisfies the equation above?

\[\large\left\lfloor \frac { x }{ 1! } \right\rfloor +\left\lfloor \frac { x }{ 2! } \right\rfloor +\left\lfloor \frac { x }{ 3! } \right\rfloor =224\]

Find the integer value of \(x\) that satisfies the equation above.

Note: \(\lfloor x \rfloor\) means the greatest integer that is smaller or equal to \(x\).

\[\Large{\lceil x^2 \rceil=\lfloor 2|x| \rfloor}\] How many integers satisfy the above equation?


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