7.4. Four pirates divided a treasure of 100 coins. It is known that among them, there are exactly two liars (who always lie) and exactly two knights (who always tell the truth).

They said:

First pirate: “We divided the coins equally.”

Second pirate: “Everyone has a different number of coins, but each got at least 15 coins.”

Third pirate: “Each person’s number of coins is divisible by 5.”

Fourth pirate: “Everyone has a different number of coins, but each got no more than 35 coins.”

What is the maximum number of coins that could have gone to one pirate?
Answer: 40 coins

Solution. Note that the first and fourth pirates could not have told the truth simultaneously.

If the first pirate is a knight, then everyone received 25 coins (such a situation is possible). In this case, the maximum number is 25.

If the fourth pirate is a knight, then each received no more than 35 coins. And in this case, the maximum number of coins is no more than 35.

If both the first and fourth pirates are liars, then the second and third pirates told the truth. Then any three pirates received no less than $15+20+25=60$ coins, so the fourth pirate received no more than 40. Such a situation is possible if the pirates received 15, 20, 35, and 40 coins. In this case, the maximum number is 40 (and the answer to the problem is 40).

Comment. The correct answer without justification - 0 points.

Identified pairs of answers that cannot be correct simultaneously - 2 points. Proved that one pirate cannot receive more than 40 coins - 3 points. Provided an example of the distribution of coins - 2 points.