Grades 7-8 Video Solutions 2024-2024_7-8

Video Transcription

Problem number 28. Captain Flint asked four of his pirates to write on a piece of paper how many gold, silver, and bronze coins there were in the treasure chest.  Their responses are shown in the diagram, but unfortunately, part of the paper was damaged. Only one of the four pirates told the truth. The other three lied in all their answers.  The total number of coins is 30. Who told the truth?  So what we can do is assume each of the pirates are telling the truth and see if we can find a contradiction or if we can find a solution that works.  Let's assume Tom is telling the truth. Since the total number of coins is 30, that means that if Tom was telling the truth, he must have written down 10 for the number of gold coins, since 10 plus 9 plus 11 equals 30.  Now, notice that we have a contradiction, because both Tom and Pitt said there are 10 gold coins. But we know that pirates will lie in all their answers if they're lying.  However, this won't be the case if Tom is telling the truth, because then Pitt's number of gold coins is also correct.  So this is a contradiction, and this means that our original assumption was wrong, that Tom was telling the truth. This means Tom cannot be telling the truth.  Now let's try the next pirate, Al. If we know that there are 30 coins, then Al should say 11 silver coins, because 30 minus 7 minus 12 is 11.  And notice that this is actually perfectly fine. None of Al's correct answers conflict with anyone else's.  Like, for example, Al says there are 7 gold coins, and nobody else says there are 7 gold coins.  Al says there are 11 silver coins, and nobody else says there are 11 silver coins, and so on.  And, in fact, we can just fill in anything else for the missing numbers, and they will work, because we know that the other pirates are lying.  So, for example, if we had 5 everywhere, then this would be a valid solution,  because Al is telling the truth, everyone else is lying, and nobody's answer is matched with any of Al's, which are the true answers.  And so in this case, we can see that Al is the one who told the truth, so the answer is B, Al.

Video Summary

The problem involves identifying which pirate among four told the truth about the number of different coins in a treasure chest, totaling 30 coins. Assuming each pirate is truthful in turn, and checking for contradictions, it was determined that Al told the truth. Al's answers did not conflict with any others when assuming the others lied entirely. Therefore, with the given constraints, Al is the truthful pirate, correctly stating the distribution of coins without contradiction.