Final answer:
In a logic puzzle with 99 people claiming 'everyone who spoke before me is a liar,' the logic dictates that all of them must be liars, leading to a total of 0 knights and 99 liars.
Step-by-step explanation:
The question presents a classic logic puzzle involving two groups of people with distinct behavioral patterns: knights who always tell the truth and liars who always lie. Given that there are 99 people on the island, the task is to determine the number of knights among them. The first person's announcement that 'we are all liars' is a crucial starting point. If this were a true statement, it would be a contradiction since a liar would be telling the truth. Therefore, this statement must be false, and the speaker is a liar.
The second person's statement that 'everyone who spoke before me is a liar' must also be a lie, as a truthful knight wouldn't be able to say this about another knight. This pattern continues such that for each of the 99 people, the strand of statements can be followed from the first person's false claim that 'we are all liars' to the conclusion that each successive person must also lie to keep the sequence valid.
To confirm this pattern, we can consider the last person's statement. If the last person were a knight, their statement would suggest there is at least one other knight who spoke before them. However, this cannot be true given the statements we have. As such, each person on the island must fabricate their statement to keep the logic consistent, which means they are all liars. Therefore, on an island with 99 people where each claims that 'everyone who spoke before me is a liar', and following the logic that a chain of liars must ensue from the first person's lie, there are 0 knights and 99 liars.