Are you as smart as a primary school kid?
EDIT: after all, this was not for primary school kids. It was for a math olympiad, in Singapore, for 14/15 year olds...
Previous iteration: #728017
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Are you as smart as a primary school kid?
EDIT: after all, this was not for primary school kids. It was for a math olympiad, in Singapore, for 14/15 year olds...
Previous iteration: #728017
Let me guess: answer is July 14.
It's not may or June because there is possibility birthday can be may 19 or June 18, in this case Bernard would know the answer but he doesn't.
Now we have July or August, so we need similar numbers in this couple (Bernard has to choose between two months), and it's 14. Now when Bernard got information that Alberts doesn't know either it's 14 or 16 we came to the answer. It's July 14
I'm still missing something, because it seems like Bernard would know the date for the 15th, 16th, or 17th, but him knowing wouldn't help Albert.
And, it seems like he doesn't have enough information to know the month if it's a 14th.
Yes now with help I found flaw in my calculations. The answer is Jule 16.
Bernard has to pairs on months with similar numbers:
When Bernard got information from Albert that he 100% should know the answer we take pair with unique number (May July), and it can't be May. So the answer is July 16
That's what I was leaning towards, but I still don't totally see it. More coffee.
At some point there's an option with 15 may or 15 august, but as Bernard final statement "I didn't know but now know", he shoude choose from month with to numbers this month is July.
June 17th
If it were June 18th, then Albert would have already known. Bernard, knowing it's June and knowing it's not the 18th, knows it must be the 17th.
Bernard knowing the date, tells Albert that it's not August, so it must be June.
How would Albert know if he only knows the month and not the day?
If Albert knows it's one of the 17th's then it's either June or August. If it were August, then Albert not knowing wouldn't be enough information for Bernard to deduce anything, because it could be any of the August dates.
Albert not knowing only eliminates the 18th and 19th as possible days, since they're the only ones unique to a month.
Eliminating the 19th would still leave two possibilities for May, so Albert knows it's not May.
The fact that Bernard can infer the answer means the date is from the month reduced to one option.
Ok, now my turn.
In the Albert eyes:
May 33% possibility Bernard knows the answers (because of unique 19)
June 50% Bernard knows (because of unique 18)
July 0% (there's no unique numbers)
August 0% (no unique numbers).
If Alberts says: Bernard doesn't know answer (read 0% chance) we need months without unique numbers.
Everything else you can follow in my first comment below
Lol, I mixed up who knows what.
So, they can cross off May and June. But, then if Bernard knows it's a 14th, he still wouldn't know which month.
This is trickier than it seems.
By statement 1, A needs to know that B doesn't know. How? Well, B can only know for sure if B sees an 18 or 19.
By statement 2, B must now know. B knows it could only be July or August.
By statement 3, A must now know.
WHEW
Finally. We collectively solve it
I think it’s July 16, but I don’t have time to explain my rationale right now. And I swear I didn’t look at others answers first
But also, what’s the deal with Cheryl?