Solution to the Four Cards problem

thescienceofdeductionandmore:

To remind you, here’s the problem:

Four cards are laid in front of you, each of which, it is explained to you, has a letter on one side and a number on the other. The sides that you see read E, 2, 5 and F. Your task is to turn over only those cards that could decisively prove the truth or falsity of the following rule: “If there is an E on one side, the number on the other side must be a 5.”

Which ones do you turn over?

Solution:

To prove the rule is true, we need to eliminate all possibilities of it being false.  In other words, we need to eliminate the possibility of an E that doesn’t have a 5 on the other side.

Obviously, we must turn over the E to make sure there’s a 5 on the other side.

We also need to turn over the 2, because if there’s an E on the other side this card will disprove the rule.

We don’t need to turn over the 5.  Whether or not there’s an E on the other side, it would still be consistent with the rule.

And we don’t need to turn over the F.  This card tells us nothing about whether the rule is true.

Solution is E and 2.

September 01, 2018 at 11:27PM