I spent a few hours today at my cousins' house practicing my trio and trying to convince my cousin Laila that (1) 0.999... equals 1, and (2) math can be cool. I convinced her on (1) and made a little headway on (2). To try to convince her further on (2), I thought of this funny math problem I came across once upon a time. I think it's cool enough to be worth posting here.
Dr. Pugh and Dr. Steel are colleagues in the math department at the University of California at Berkeley. One day they are at a math department party and their student, Mason, says, "I have an amusing little problem for you. I'm thinking of two whole numbers between 1 and 9, inclusive. Their product is [he whispers something in Pugh's ear] and their sum is [he whispers something in Steel's ear]. Can you figure out what the numbers are?"
They both take out pencil and paper and do some calculations.
Then Pugh says, "Hmm... no, I don't know."
Then Steel does some more calculations and says, "Hmm... no, I don't know."
Then Pugh does some more calculations and says, "Hmm... no, I still don't know."
Then Steel does some more calculations and says, "Hmm... no, I still don't know."
Then Pugh does some more calculations and says, "Hmm... no, I still don't know."
Then Steel does some more calculations and says, "Hmm... no, I still don't know."
Then Pugh does some more calculations and says, "Hmm... no, I still don't know."
Then Steel does some more calculations and says, "Hmm... no, I still don't know."
Then Pugh does some more calculations and says, "AHA!"
What are the two numbers?
If you know, don't give it away in the comments. If you're stuck and need a hint, email me (clobberfoe of geemale).
2 comments:
If Pugh and Steel both thought that the "two whole numbers between 1 and 9, inclusive" had to be different numbers, can Pugh and Steel determine the numbers? If so, how many IDK's (again starting with Pugh) would occur before forcing an Aha?
If we assume that the two numbers are the same in your scenario as in my original scenario, then Pugh would get the answer right away (and Steel would never get it). Using different numbers for your scenario, the maximum number of IDK's is 3 (Pugh, then Steel, then Pugh) before one of them (Steel in this case) knows the answer.
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