Let $\lfloor x \rfloor$ denotes the greatest integer less than or equal to $x$. Find $x$ such that $x\lfloor x\lfloor x\lfloor x\rfloor\rfloor \rfloor = 88$
[list=1]
[*] $\pi$
[*] 3.14

[*] $\frac{22}{7}$

[*] All of these
[/list]
1. We start with the given equation:
   \[
   x \lfloor x \lfloor x \lfloor x \rfloor \rfloor \rfloor = 88
   \]
   Let \( \lfloor x \rfloor = n \), where \( n \) is an integer. Then we can rewrite the equation as:
   \[
   x \lfloor x \lfloor x \lfloor x \rfloor \rfloor \rfloor = 88
   \]
   This implies:
   \[
   \lfloor x \lfloor x \lfloor x \rfloor \rfloor \rfloor = \frac{88}{x}
   \]
   Since \( \lfloor x \lfloor x \lfloor x \rfloor \rfloor \rfloor \) must be an integer, \( \frac{88}{x} \) must also be an integer. Therefore, \( x \) must be a rational number.

2. Let \( x = \frac{a}{b} \) where \( \gcd(a, b) = 1 \). We need to find \( x \) such that:
   \[
   \lfloor x \lfloor x \lfloor x \rfloor \rfloor \rfloor = \frac{88}{x}
   \]
   Since \( \frac{88}{x} \) is an integer, \( a \) must be a divisor of 88.

3. Consider the case \( x > 0 \):
   - We must have \( \lfloor x \rfloor = 3 \) because \( 3 \leq x < 4 \).
   - This implies \( 9 \leq 3x < 12 \) and \( 27 \leq 9x < 36 \).
   - Therefore, \( \lfloor x \lfloor x \lfloor x \rfloor \rfloor \rfloor = \lfloor x \lfloor 3x \rfloor \rfloor \).

4. We also have:
   \[
   \frac{88}{3} \geq \frac{88}{x} > 22
   \]
   This implies:
   \[
   \lfloor x \lfloor 3x \rfloor \rfloor \in \{23, 24, \ldots, 28\}
   \]
   Notice that \( \lfloor x \lfloor 3x \rfloor \rfloor \) can only equal 28 because:
   \[
   7 \leq 9x < 36
   \]
   We must have \( \frac{88 \cdot b}{a} \) to be an integer. Hence:
   \[
   \frac{88 \cdot b}{a} = 28 \implies \frac{a}{b} = \frac{22}{7} \implies x = \frac{22}{7}
   \]

5. Consider the case \( x < 0 \):
   - Set \( x = -3 - \delta \) for \( \delta \in [0, 1) \).
   - We notice that there is no such \( x \) that works in this case.

Hence, on concluding, we have only one solution and that is:
\[
\boxed{\frac{22}{7}}
\]