Ceilings, floors

Algebra Level 2

$2019 = \left \lceil x \right \rceil + \left \lfloor x \right \rfloor + \left \{ x \right \}$

What is $x$ ?

If you think there is no answer, enter $0$ .

1 solution

Geoff Pilling
Jan 2, 2019

Since the ceiling and floor of $x$ must be integers, $\left \{ x \right \} = 0$ , so $x$ is an integer.

For an integer, $\left \lceil x \right \rceil + \left \lfloor x \right \rfloor = 2x$ .

But 2019 is odd, so no solution exists.