“I know that you know that I don’t know” seems like a pointless clue… yet it is sometimes enough to discover the truth, as the following riddle shows.
Albane and Béatrice have just bondedfriendship with Caroline and would like to know the date of her birthday. They know there’s only ten dates possible: 15, 16 or 19 May, 17 or 18 June, 14 or 16 July and 14, 15 or 17 August. Caroline gives Albane the month and Béatrice the day of her birthday.
Alban then says: I don’t know the date of Caroline’s birthday, but neither do I know Béatrice.
Beatrice responds: I didn’t know when Caroline’s birthday was but now I know.
Albania: now I know it too.
Answer :
July 16. Albane cannot conclude because she only knows the month and several days are possible for each month. On the other hand, she knows that Beatrice could conclude if the day was the 19th or the 18th because these days each correspond to a single possible month: May and June respectively. Caroline’s birthday is therefore in July or August. If Béatrice knows now, it’s because the day she knows only appears once between the months of July and August, so it’s July 16 or August 15 or 17. If she’s sure of the birthday, it’s July 16th. Knowing that Beatrice understood what was the date of theanniversaryAlbane understands that the date is July 16.
Learn more about Hervé Lehning
Ecole Normale Normale and maths graduate, Hervé Lehning taught his discipline for a good forty years. Mad about cryptography, member of the Association of encryption and information security reservists, he has in particular pierced the secrets of Henri II’s cipher box.
- His blog MATH’WORLD on Futura
- the latest book by Hervé Lehning :
Also to discover: The universe of secret codes from Antiquity to the Internet published in 2012 by Ixelles.
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