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January 2nd, 2017, 11:20 AM   #21
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Quote:
Originally Posted by rachel1234 View Post

Problem 3)
George, Harry, and Ethan are perfect logicians that always tell the truth. George decides to pose a puzzle to his friends: he tells them that the day of his birthday is at most the number of the month of his birthday. Then George announces that he will whisper the day of his birthday to Harry and the month of his birthday to Ethan, and he does exactly that.

After George whispers to both of them, Harry thinks a bit, then says “Ethan cannot know
what George's birthday is.”

After that, Ethan thinks a bit, then says “Harry also cannot know what George's birthday
is.”

This exchange repeats, with Harry and Ethan speaking alternately and each saying the other can’t know George's birthday. However, at one point, Ethan instead announces “Harry and I can now know what George's birthday is. Interestingly, that was the longest conversation like that we could have possibly had before both figuring out George's birthday.”

Find George's birthday.
G H E
B d m
assume m=7

H assumes m=1
E replies H doesn't know.

H assumes m=2
E replies H doesn't know.
.
.
H assumes m=7
E replies they have figured it out.

They are just keeping track of the number of repeat responses, whatever the response is.
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January 2nd, 2017, 07:38 PM   #22
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Guys, stop helping her.
This isn't for fun. It's for the USA mathematical talent search competition. It's not right to help her for a competition.
Link - http://usamts.org/Tests/Problems_28_3.pdf
Thanks from quasi

Last edited by skipjack; January 2nd, 2017 at 08:08 PM.
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