I issue a courtesy warning that a dab of geometry crops up in the solution. Don’t let it deter you from discovering the ingenious method. If you remember the Pythagorean theorem, then you know all you’ll need.
I will post the solution next Monday along with a new puzzle. Do you know a great puzzle that I should cover here? Send it to me at gizmodopuzzle@gmail.comfrom a seemingly uninformative conversation.Alicia and Bruno are each given a different natural number in secret . They are then tasked with guessing which of them has the larger number. The following conversation ensues:Alicia: Upon further reflection, I remain ignorant.
Did you work out that Alicia had 4 and Bruno had 5? What can both parties infer as each line of the conversation unfolds? When Alicia opens with, “I don’t know who has the bigger number,” Bruno now knows that Alicia cannot have 1, because if Alicia had 1, then she would know that Bruno has the bigger number! Remember, they’re given different numbers, and 1 is the smallest they could have received.Bruno says, “I don’t know either.
doesn’t suffice for Alicia to determine who has the larger number. If Alicia had 2 or 3, she would know that Bruno had the larger number. So in addition to not having 1, Alicia must not have 2 or 3 either. In turn, Bruno’s subsequent admission of uncertainty “Alas, I’m still unsure too” confirms that he doesn’t have 3 or 4.Upon learning that Bruno does not have 3 or 4, Alicia suddenly knows who has the larger number.
Bruno: “Cool! In that case, I know what both of the numbers are.” We know Bruno’s number is larger than 4. If Bruno had 6 or above, how could he figure out whether Alicia has 4 or 5? He couldn’t. So Bruno must have 5, leaving Alicia with 4.