Ceilings? Floors?

Number Theory Level pending

\(\left \lceil x \right \rceil + \left \lfloor x \right \rfloor + \left \{ x \right \} = 6\)

How many different values for \(x\) are there?

Clarification:

  • \(\left \lceil x \right \rceil\) is the ceiling of \(x\)
  • \(\left \lfloor x \right \rfloor\) is the floor of \(x\)
  • \(\left \{ x \right \}\) is the fractional part of \(x\)
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