Charlie’s Birthday

Charlie presents a list of 14 possible dates for his birthday to Albert, Bernard, and Cheryl.

Apr 14, 1999
Feb 19, 2000
Mar 14, 2000
Mar 15, 2000
Apr 16, 2000
Apr 15, 2000
Feb 15, 2001
Mar 15, 2001
Apr 14, 2001
Apr 16, 2001
May 14, 2001
May 16, 2001
May 17, 2001
Feb 17, 2002

He then announces that he is going to tell Albert the month, Bernard the day, and Cheryl the year.

After he tells them, Albert says, “I don’t know Charlie’s birthday, but neither does Bernard.”

Bernard then says, “That is true, but Cheryl also does not know Charlie’s birthday.”

Cheryl says, “Yes, and Albert still has not figured out Charlie’s birthday.”

Bernard then replies, “Well, now I know his birthday.”

At this point, Albert says, “Yes, we all know it now.”

What is Charlie’s birthday?

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NerdyPotato ·

Another try: if the 3rd clue is about the day number rather than the full date, then I can eliminate it further to May 17, 2001.

DunningKruger · 61-69, M

@NerdyPotato No, I'm afraid not.

NerdyPotato ·

@DunningKruger ah, I was too quick in my 4th step. My reasoning:

After he tells them, Albert says, “I don’t know Charlie’s birthday, but neither does Bernard.”

If the day were 19, Bernard would know, so it isn't. Albert would only know that if the month wasn't February.

That leaves us with:
Apr 14, 1999
Mar 14, 2000
Mar 15, 2000
Apr 16, 2000
Apr 15, 2000
Mar 15, 2001
Apr 14, 2001
Apr 16, 2001
May 14, 2001
May 16, 2001
May 17, 2001

Bernard then says, “That is true, but Cheryl also does not know Charlie’s birthday.”

If the year were 1999, Cheryl would know, so it isn't. Bernard would only know that if the day wasn't 14.

That leaves us with:
Mar 15, 2000
Apr 16, 2000
Apr 15, 2000
Mar 15, 2001
Apr 16, 2001
May 16, 2001
May 17, 2001

Cheryl says, “Yes, and Albert still has not figured out Charlie’s birthday.”

If the month was March, the day would have to be 15 so it can't be March.

That leaves us with:
Apr 16, 2000
Apr 15, 2000
Apr 16, 2001
May 16, 2001
May 17, 2001

Bernard then replies, “Well, now I know his birthday.”

He would still be left with multiple options if the day were 16, so it isn't.

That leaves us with:
Apr 15, 2000
May 17, 2001

At this point, Albert says, “Yes, we all know it now.”

Indeed: any piece (month, day or year) will differentiate between the two. We don't have any of those though, so for us it could still be either, unless I'm missing something.

Also: how did Cheryl know Albert was still struggling with the day? It could be March and therefore 15 with either of the remaining years. 🤔

DunningKruger · 61-69, M

@NerdyPotato I'm afraid neither of your options is the correct answer.

DunningKruger · 61-69, M

@DunningKruger You're on the right track, though.

NerdyPotato ·

@DunningKruger let's try this again then 😅 I think I've identified one piece of information I missed.

After he tells them, Albert says, “I don’t know Charlie’s birthday, but neither does Bernard.”

1a. Albert doesn't know = correct month isn't unique.
True for all, no eliminations

1b. Bernard doesn't know = correct month doesn't have any unique day
False for Feb (19), so Feb eliminated

Apr 14, 1999
Mar 14, 2000
Mar 15, 2000
Apr 16, 2000
Apr 15, 2000
Mar 15, 2001
Apr 14, 2001
Apr 16, 2001
May 14, 2001
May 16, 2001
May 17, 2001

Bernard then says, “That is true, but Cheryl also does not know Charlie’s birthday.”

2a. Bernard still doesn't know = correct day isn't unique
False for 17, so eliminated (missed that one earlier)

Apr 14, 1999
Mar 14, 2000
Mar 15, 2000
Apr 16, 2000
Apr 15, 2000
Mar 15, 2001
Apr 14, 2001
Apr 16, 2001
May 14, 2001
May 16, 2001

2b. Cheryl doesn't know = correct day doesn't have any unique year
False for 14 (1999), so 14 is eliminated

Mar 15, 2000
Apr 16, 2000
Apr 15, 2000
Mar 15, 2001
Apr 16, 2001
May 16, 2001

Cheryl says, “Yes, and Albert still has not figured out Charlie’s birthday.”

3a. Cheryl doesn't know = correct year isn't unique.
True for all, no eliminations

3b. Albert doesn't know = correct year doesn't have any unique month
False for 2001 (May), so eliminated

Mar 15, 2000
Apr 16, 2000
Apr 15, 2000

Bernard then replies, “Well, now I know his birthday.”

4. Bernard knows = day is unique = 16
All dates with a different day are eliminated

Apr 16, 2000

At this point, Albert says, “Yes, we all know it now.”

Indeed we do!

DunningKruger · 61-69, M

@NerdyPotato

Congratulations! Your prize is in the mail.

NerdyPotato ·

@DunningKruger it was a tricky one with the same statement twice in a row having a different meaning after processing it once, but that made it all the more fun. Riddles are good, but being wrong first makes it all the better to be right afterwards.