A logician decides to test three students named Rich, Ken and Rob. He said:
I am thinking of the initials of a full name. First, middle and last. On three separate blank cards I have written those initials. Rich gets the initial for the first name, Ken gets the initial for the middle name and Rob gets the initial of the last name.
Then on the board he shows them a table of the three initials. He tells them that the name's initials is one of these 10 choices.
|FIRST INITIAL||MIDDLE INITIAL||LAST INITIAL|
He asks, "Can you guess the correct combination?"
Rich looks at his card and says, “I cannot logically guess the combination.”
Ken looks at his card and says, "I also cannot guess the combination."
Rob looks at his card and says, "I know the combination!"
Rich says, "OK. So I know the combination also."
Ken after thinking a bit says, "I definitely know the combination but the other two are wrong!"
The logician asks them to write down their guesses and sure enough Ken was right. Explain what must have happened assuming nobody lied. What was the correct combination?