Albert and Bernard just became friends with Cheryl, and they want to know her birthday. Cheryl gives them a list of 10 possible dates:
| May 15 | May 16 | May 19 |
| June 17 | June 18 | |
| July 14 | July 16 | |
| August 14 | August 15 | August 17 |
Cheryl then tells Albert the month, and Bernard the day.
- Albert: I don't know the birthday, but I know that Bernard also doesn't know.
- Bernard: At first I didn't know the birthday, but now I know.
- Albert: Then I also know the birthday now.
What is Cheryl's birthday?
Bounty: 1,000 sats to the correct answer with the best explanation. Suspected AI use will be ignored.
Source: I forgot. I've had this in my repertoire for a while now.
1,000 sats paid
Here's how I work it out step by step.
If May XX:
If June XX:
If August 14
If August 15
If August 17
If July 14
If July 16
Conclusion: July 16 is the only one that is consistent with the pattern of facts.
Hate to brag but it’s a Singapore question. Maths Olympiad meant for 14/15-year-old teens
And nope, I don’t think I can solve this. Haha. Neither do I really care
It's a beautiful puzzle because it doesn't actually involve any complex math. Just basic logic, but you do have to be very careful with it.
since I’m immersed in the system, I’m wringing my hands and thinking why children must be put through such questions that seem to have little relevance to life. but you seem to approve them because of the thinking skills that underpin the solutions
I don't know if I approve of it as a standardized test question. It's kind of like putting "run a 5 minute mile" on a physical fitness test meant for the general population: quite unfair to most regular people.
But as a competition question I think it's definitely fair.
This puzzle everytime blows my mind.
It lefts us with June and August, because these months without unique date.
Now we have 15, 16 and 17. If it was 14 Bernard still wouldn't know the right answer.
At this point we're at the trap. Seem like it's July 16, because if we eliminate 14th date we left with 16, but as I remember the right answer if 17. Logic Behind it, we take the month with unique date where we have only two options and it's June. If it's not 18, then it's 17. Get back to possible months (July and August), with 17 we have only August. So the right answer should be August 17.
p.s. I really want to read right explanation without googling or AI-ing.
You almost got it but psyched yourself out by thinking the answer should be 17.
Yeah, you're right I went to the incorrect solution of ired the most obvious answer.
btw, there's even a page on wiki dedicated to this puzzle https://en.wikipedia.org/wiki/Cheryl%27s_Birthday
June 17
Force it to drop the 18th and 19th.
It has to be June, because that's the only option left.
The problem with your logic is that if the birthday was June 17, how would Albert be so confident that Bernard doesn't know the birthday?
Albert sees only June. From his perspective, it's possible that the birthday is June 18, in which case Bernard would know simply by seeing 18.
July 16.
After Albert's first sentence, it has to be July or August (since in May or June, there are days 18/19 that occur only once, in which case Bernard would know the date immediately).
Bernhard also infers from the same logic that it has to be July or August. Further, the day cannot be 14, since then Bernhard still wouldn't know in the second step (cannot decide between July 14 or August 14), but he claims to know.
That leaves July 16, August 15 or August 17. Albert, following up to here, then claims to know the date. If it were August, there would still be two choices and Albert wouldn't know. So it has to be July 16.
Disclaimer: I think I've seen a similar puzzle before, but I had to think about it again.
Congratulations, this is the correct answer! I will post my own explanation above.
Thanks!