FiveThirtyEight's Riddler

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April fools day leads to many hilarious pranks, some go to far and some are unbelievable in the fact anyone believed them in the first place.  But instead of going down that endless well, I am going to tackle this week’s riddle from FiveThirtyEight.com.

Here it is so you don’t have to click over (in case you would like to):

Three very skilled logicians are sitting around a table — Barack, Pete and Susan. Barack says: “I’m thinking of two natural numbers between 1 and 9, inclusive. I’ve written the product of these two numbers on this paper that I’m giving to you, Pete. I’ve written the sum of the two numbers on this paper that I’m giving to you, Susan. Now Pete, looking at your paper, do you know which numbers I’m thinking of?”
Pete looks at his paper and says: “No, I don’t.”
Barack turns to Susan and asks: “Susan, do you know which numbers I’m thinking of?” Susan looks at her paper and says: “No.”
Barack turns back to Pete and asks: “How about now? Do you know?”
“No, I still don’t,” Pete says.
Barack keeps going back and forth, and when he asks Pete for the fifth time, Pete says: “Yes, now I know!”
First, what are the two numbers? Second, if Pete had said no the fifth time, would Susan have said yes or no at her fifth turn?

Please stop reading if you want to give it a try yourself…

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All right, if you are here I hope you at least gave the problem a shot.  This week’s riddle was pretty straightforward.  If you just mapped all the possible combinations of products and sums for the numbers 1 through 9, it becomes pretty easy to remove any answer that is unique and would lead to a "yes".  The numbers are 2 and 8.  Here is the answer mapped out by each “no” and the final "yes" (non-unique answers are in bold and are not removed by said "no"):

The only unique solution is 2 and 8 at this point.  Another no would have led to never knowing the correct answer since 1,8; 1,9; 2,4; 2,8; 2,9; 3,3; 3,6; 3,8; and 4,6 were still possibilities.

Most weeks the puzzle is not this straightforward, but just having a weekly riddle is a fun break to start the weekend.  While I will not be posting about the riddler on a weekly basis, I did want to post at least once about the weekly Riddler.  It is a fun brain exercise and a shout out FiveThirtyEight, one of the best websites out there.