**Problem Analysis**

We are given that the highest common factor (HCF) of two numbers is 11 and their least common multiple (LCM) is 9900. We need to find the other number if one of the numbers is 326.

**Solution**

To solve this problem, we need to understand the relationship between the HCF, LCM, and the actual numbers.

Let's assume the other number is 'x'. Given that the HCF of the two numbers is 11, we can write:

326 = 11a (where 'a' is an integer)

Dividing both sides of the equation by 11, we get:

a = 29

Now, let's find the LCM of 326 and 'x'. We are given that the LCM is 9900, so we can write:

LCM(326, x) = 9900

To find the LCM, we need to factorize the numbers 326 and 'x' into their prime factors.

326 = 2 * 163
x = p1^a1 * p2^a2 * p3^a3 * ... * pn^an

Since the HCF of 326 and 'x' is 11, we know that the prime factorization of 'x' should contain 11 as a factor. Therefore, we can write:

x = 11 * q1^b1 * q2^b2 * q3^b3 * ... * qn^bn

where 'q1', 'q2', 'q3', etc. are prime factors other than 11, and 'b1', 'b2', 'b3', etc. are their respective powers.

Now, let's write the LCM in terms of the prime factorization of 326 and 'x':

LCM(326, x) = 2 * 163 * 11 * q1^b1 * q2^b2 * q3^b3 * ... * qn^bn

Since the LCM is given as 9900, we can equate the two expressions:

2 * 163 * 11 * q1^b1 * q2^b2 * q3^b3 * ... * qn^bn = 9900

Dividing both sides of the equation by 2 * 11, we get:

163 * q1^b1 * q2^b2 * q3^b3 * ... * qn^bn = 450

The prime factorization of 450 is:

450 = 2 * 3^2 * 5^2

Comparing the prime factorizations on both sides of the equation, we can conclude that:

163 = 3^2 * 5^2

This is not possible since 163 is a prime number. Therefore, there is no possible value for 'x' that satisfies the given conditions.

**Conclusion**

Based on the given information, there is no possible value for the other number if one of the numbers is 326.