A question from a global maths Olympiad for high school children in Singapore is going viral after the question was leaked online.
The question seems simple — all you need to do is work out Cheryl’s birthday, based on three statements and with just 10 possible dates to chose from — but the logic to solving it will really make your brain crinkle.
Here’s the question in plain text:
Albert and Bernard just became friends with Cheryl, and they want to know when her birthday is. 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 and Bernard separately the month and the day of her birthday respectively.
Albert: I don’t know when Cheryl’s birthday is, but I know that Bernard does not know too.
Bernard: At first I don’t know when Cheryl’s birthday is, but I know now.
Albert: Then I also know when Cheryl’s birthday is.
So when is Cheryl’s birthday?
Think you know the answer? The question prompted so much confusion that the creators of the test posted an explanation on Facebook to clarify matters.
The official solution is below, however, some commenters have found the logic even more confusing than the question itself, so we’ve broken it down even further below.
If that solution confused you, we’ve broken it down piece-by-piece here:
- At the start, Albert and Bernard are each given one piece of information about Cheryl’s birthday, which isn’t enough in isolation to work out when it is.
- To begin with, Bernard knows the day (but not the month) the birthday falls on. This means we can rule out May 19 and June 18 straight away — these days (18 & 19) occur only once in the list of dates, so if it were one of them, he would be able to infer the month by knowing only the day. (In contrast, 14, 15, 16, and 17 all appear twice.)
- But Albert knows that Bernard — initially — does not know the birthday. How? Well, Albert knows the month it falls in. Had Cheryl told him May or June, then it’s possible (but not guaranteed), that Bernard already knows the date. But Albert knows that Bernard doesn’t know the full date, which means Cheryl must have told Albert that the month is either July or August.
- Bernard realises what the date is after Albert first says that he knows that Bernard doesn’t know it. How does this work? Once Albert says that Bernard doesn’t know, it shows to Bernard that it can’t be in May or June. (After all, if it was, then Albert wouldn’t know that Bernard doesn’t know.) So this leaves July and August. Now, remember that Bernard knows the day (but not the month). Of the 5 options, 14 is the only one repeated twice. If it were July 14 or August 14 he still wouldn’t know — but he does know, which means the day he was told must have been 15, 16, or 17, and we can cross another two possibilities out.
- And then, after Bernard realises what the date is, Albert follows suit. This is because — as we’ve established — Albert knows only the month. With 3 options left, if Albert had been told it were in August, he still wouldn’t know, because there are 2 August options left. But that’s not the case — Albert does know with certainty what date it is. From this we can infer that it is July 16, as there’s only one July option there.
To recap, Albert was told that Cheryl’s birthday was in July, while Bernard was told it landed on the 17. This limited knowledge allowed each to narrow down their options — and by making inferences from the other’s ignorance, the two could continue to thin down the possible categories until there was only one option left.
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