Perfect Information

Hello there,

I have a really problem to understand here :

https://brilliant.org/practice/perfect-information/?p=5

"However, since Albert knows that Bernard doesn’t know, Cheryl’s birthday can’t be in May or June. Since Albert knows the month but not the day, the only way he can be certain that Bernard doesn’t know is if Cheryl’s birthday is not in May or June, which means it must be in July or August."

My question : Why Cheryl's birthday can't be in June or May ? Ok, we know if Cheryl gave him the 18th or 19th date he would know that the birthday was in May 19 or June 18, but why make exclude totally the possiblity that all the reaminning days of the two months ?

Note by Ahmed Chikh
6 months, 1 week ago

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Comments

So you got three possible dates that you think is still possible: May 15, May 16, June 17.

Case 1: Suppose it's May 15.

  • Albert got MAY, Bernard got 15.

  • Albert's first line of I don't know when Cheryl's birthday is, but I know that Bernard does not know either. holds.

  • But even after Albert said this, Bernard cannot possible say At first I didn't know when Cheryl's birthday is, but I know now. because he still can't narrow down Cheryl's birthday: May 15 or August 15.

Case 2: Suppose it's May 16.

  • Albert got MAY, Bernard got 16.

  • Albert's first line of I don't know when Cheryl's birthday is, but I know that Bernard does not know either. holds.

  • But even after Albert said this, Bernard cannot possible say At first I didn't know when Cheryl's birthday is, but I know now. because he still can't narrow down Cheryl's birthday: May 16 or July 16.

Case 3: Suppose it's June 17.

  • Albert got JUNE, Bernard got 17.

  • Albert's first line of I don't know when Cheryl's birthday is, but I know that Bernard does not know either. holds.

  • But even after Albert said this, Bernard cannot possible say At first I didn't know when Cheryl's birthday is, but I know now. because he still can't narrow down Cheryl's birthday: June 17 or August 17.

All three cases does not match the Bernard's claim.

Pi Han Goh - 6 months, 1 week ago
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