Floor and Ceiling Functions

Floor and Ceiling Functions: Level 3 Challenges


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

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

2x34=5\left\lfloor \left| \frac{2x-3}{4} \right| \right\rfloor = 5

What is the largest negative integer xx that satisfies the equation above?

x1!+x2!+x3!=224\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 xx that satisfies the equation above.

Note: x\lfloor x \rfloor denotes the greatest integer that is smaller than or equal to xx.

x2=2x\Large{\lceil x^2 \rceil=\lfloor 2|x| \rfloor} How many integers satisfy the above equation?


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