These problems are from a very large set of questions about Liars who always lie about everything, and Knights who always tell the truth. Some questions also involve Knaves - people who strictly alternate between lying and telling the truth. (They are of course all indistinguishable from one another by outward appearance, and you must use logic to determine who's who.)
In a remote island, three people Abe, Ben and Cal took part in a running race. They belong to three different types: Knights, who always tell the truth; Liars who always lie and, Knaves who alternatively tell a truth or lie. It is known that precisely one of Abe, Ben and Cal is a knight, precisely one of them is a liar and the remaining is a knave. It is also known that there was precisely one person who reached the first position in the said race.
Following are some statements made by them:
Abe
1. I would have won the race if Cal had not come in my way to restrain me in the final part.
2. Cal won the race.
Ben
1. I won the race.
2. Cal came in Abe’s way, to restrain him from winning the race.
Cal
1. Ben won the race.
2. I did not come in Abe’s way, to restrain him from winning the race.
Find the types each of the three men belong to. Who won the race?
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