Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Kindly asking to find the set of possible solutions if they exist of the equation $$\lfloor x+\lfloor x+\lfloor x\rfloor\rfloor\rfloor+3\lfloor x\rfloor=18$$ Of course I have 4 intervals as choices:

  1. $[\frac{5}{2}, \frac{7}{2})$
  2. $[3, 5)\smallsetminus \{4\}$
  3. $[3, 4)$
  4. $\emptyset$

$\lfloor x\rfloor$ is largest integer not greater than $x$. Thank you very much.

share|improve this question
    
It seems to me that $x=3$ is a solution, while $x=5/2$ is not. This should exclude 1 and 4. –  Siminore Jun 24 '12 at 12:48

1 Answer 1

up vote 7 down vote accepted

Hint: show that if $n$ is an integer, and $r$ is any real number, then $$\lfloor r+n\rfloor=\lfloor r\rfloor+n.$$ Apply this to the expression $\lfloor x+\lfloor x+\lfloor x\rfloor\rfloor\rfloor$.

share|improve this answer
    
I should have considered that [r+n]=[r]+n. Thank you –  Ned Dabby Jun 24 '12 at 13:01

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.