Problem 1071

"My day of birth is an integer D which can range from 1 to 12, less than or equal to my month of birth M".

Cédric then announces that he will indicate the day to Alice and the month to Bob. Once her promise is fulfilled, Alice says:

"I know Bob cannot know his birthday."

Bob says the same for Alice. In turn, each of the two accomplices says that the other cannot guess the birthday at this stage of the information.

The exchange is as long as possible, until Alice declares "Bob will be able to guess it, me, I have just done it".

• 1. What is Cédric's birthday? (8 points) (we will answer the number of 3 or 4 digits equal to 100 D + M)

Annie, meanwhile, announces that her birth month is strictly inferior to her day of birth, but they both end in the same figure and she will give one to Alice, the other to Bob without specifying which one.

Alice: "I can not guess, but I know Bob cannot either."

Bob: "Indeed, I cannot guess, but I know if the number Annie told me is the day or the month"

Alice: "Then I know the date".

Bob: "Me too".

• 2. What is Annie's birthday? (8 points)

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See answer