7 Days of Christmas: Day 7!

One of the most controversial problems in mathematics this year that went viral was a problem for Singaporean secondary school students asking, “When is Cheryl’s Birthday?”

To figure this out, we’re given the following information:

7.jpg

So how do we solve it?

We must remember two facts:

  • Albert is told that it’s either in May, June, July or August.
  • Bernard is told that it’s either on the 14, 15, 16, 17, 18 or 19

Albert: I don’t know when Cheryl’s birthday is, but I know that Bernard doesn’t know too.

We can deduce that the only way Bernard could know the date with a single number, would be if Cheryl had told him 18 or 19, since of the ten date options only these numbers appear once (as May 19 and June 18). For Albert to know that Bernard does not know, Albert must therefore have been told July or August, since this rules out Bernard being told 18 or 19.

Bernard: At first I don’t know when Cheryl’s birthday is, but now I know.

Bernard has deduced that Albert has either August or July and if he knows the full date, he must have been told 15, 16 and 17 as they refer to one specific month, but 14 could be either month.

Albert: Then I also know when Cheryl’s birthday is.

Therefore, Albert has figured out that the possible dates are July 16, August 15 and August 17. For him to now know, he must have been told July, since if he had been told August he would not know which date for certain is Cheryl’s birthday.

Hence, the answer is July 16.

To read day 6, click here.

Merry Christmas everyone! M x

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3 comments

  1. It’s a great puzzle. I may be remembering wrong but believe the problem was for a Maths Olympiad style contest rather than ordinary secondary school students, though. This makes it easier to me thinking how long I needed to solve it.

    Like

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