The correct answer is option 'C': By measuring height one by one.

Explanation:
In order to understand how the public demand was fulfilled, it is important to analyze the options provided in the question.

a) By voting: Voting is a common method used to make decisions in a democratic society. However, in the context of this question, it is not mentioned that voting was used to fulfill the public demand. Therefore, this option can be eliminated.

b) By the King's discretion: This option suggests that the King made the decision on his own without consulting the public. However, the question states that the public demand was fulfilled, indicating that the public had a say in the decision-making process. Hence, this option can be ruled out.

c) By measuring height one by one: This option implies that the public demand was fulfilled by taking individual measurements of height. While it may seem unusual to fulfill a public demand through such a method, the question specifies that this is the correct answer.

By measuring height one by one, it could be inferred that the public demand was related to the physical characteristics of individuals. It is possible that the demand was for a specific requirement or qualification based on height. By measuring the height of each individual, the demand could have been fulfilled by ensuring that those who met the height criteria were selected or granted a particular privilege.

d) By the councillors' decision: This option suggests that the decision was made by a group of councillors. However, it does not provide any information about the involvement of the public in the decision-making process. Therefore, this option can be eliminated.

In conclusion, based on the options provided, the correct answer is option 'C': By measuring height one by one. Although it may seem unusual, this method was used to fulfill the public demand.