hmsies.

Cultural experiences and funny musings by two twenty-somethings living abroad

How Cheryl Got The World Scratching Their Heads

puzzled

A little logic problem has been making its rounds on the interwebs lately about the story of Cheryl’s birthday, and Albert’s and Bernard’s challenge to find out when it is. This question cropped up in a school exam in Singapore for 14-15 year olds, yet it would leave most adults across the world stumped. In case you haven’t seen the question yet, this is what it looks like

cheryls bday

 

Just to clear up some of the wording, it is Albert who has been told the month of her birthday, and it is Bernard who was told the day (or number) of her birthday.

So Albert and Bernard have a little conversation basically going along the lines of “I don’t know, but I know he doesn’t know”, “I didn’t know, but I know now”, “Then if you know, I know”. And from these three phrases, we are supposed to be able to work out when Cheryl’s birthday is… somehow.

If you fancy it, try giving this question a shot! If you get stumped though, scroll down to find our solution!

 


 

So here’s the solution!

The first thing to note straight away is that eight of those ten dates share the same number with another date in that set, and only two of those dates have a unique number – May 19th and June 18th. If Bernard had been told either the 18th or the 19th, he would have known when Cheryl’s birthday is straight away and would have said so, but he doesn’t say that he knows, meaning he can’t have been told “18” or “19”. Therefore we can rule out those two dates, leaving us with:

May 15th May 16th May 18th

June 17th June 18th

July 14th July 16th

August 14th August 15th August 17th

 

Albert, who is the person who knows the month and now knows that Bernard can’t have been told “18” or “19”, then says “I don’t know when Cheryl’s birthday is…”. By saying that, he effectively rules out June, because June 17th is the only possible date left in that month, otherwise he would know when her birthday is. But then he also says “…but I know that Bernard doesn’t know too”. By saying that, he also rules out the dates in May, otherwise Bernard could work out it is either May 15th or May 16th. That therefore leaves:

 

May 15th May 16th May 18th

June 17th June 18th

July 14th July 16th

August 14th August 15th August 17th

 

At this stage, only two of the dates now share the same number, July 14th and August 14th, and three of the dates now have a unique number after ruling out the dates in May and June. Bernard now says “At first I don’t know when Cheryl’s birthday is, but I know now”. That means Bernard must have been told a number that is unique – if he had been told “14”, he couldn’t say he knows when Cheryl’s birthday is because it could have been either July 14th or August 14th, so he must have been told either “15”, “16” or “17”. That then leaves us with:

 

May 15th May 16th May 18th

June 17th June 18th

July 14th July 16th

August 14th August 15th August 17th

 

Albert, who now knows the number can’t be “14”, is now able to say “Then I also know when Cheryl’s birthday is”. That means he must have been told her birthday was in July because there is only one possible date remaining in that month – if he said he still didn’t know, then he would have been told it was in August, as there are still two possible dates left.

 

That therefore leaves one date, and Cheryl’s birthday falls on July 16th

 

And the moral of the story is that Albert and Bernard need to find better friends.

Advertisements

Let us know what you think!

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

Information

This entry was posted on April 15, 2015 by in Things that make us go 'hmmmm' and tagged , , , , , , , .
%d bloggers like this: