And its’ Cheryl’s Birthday! #CherylsBirthday


Well we dont know the the date yet But you will know by the end of this post!! So This question is a reasoning based Math problem posted by Kennethjianwen on FB, was question in  Singapore and Asian School Math Olympiads‘s Math Olympiad!

cheryl'sBirthday

The Question seems tricky but once you figure out the trick Question becomes fun and interesting! So lets get started!!

First of I would give credit to Khan Academy video for helping me with the trick.

So the Trick is: WRITE DOWN THE FACTS!

Yes thats the trick! Confused?? Let me tell you how…

Albert, Benard and Cheryl are friends. Cheryl has told the Month of her birthday to Albert and Date to Benard! And 10 possible dates are given! 

So lets see what Albert Knows:

Month               Possible dates

May                   15, 16, 19

June                  17, 18

July                   14, 16

Aug                   14, 15, 17

And what Benard knows:

Date                Possible Month

14                    July, Aug

15                    May, Aug

16                    May, July

17                    June, Aug

18                    June

19                     May

Now its clear from Benards’ information that if the date is 18 or 19, Benard will know the birthday date and month immediately, as there are only 1 options for those. And clearly Albert does not know because there are multiple dates for every month.

But look at the conversation between Benard and Albert,

Albert says:  I dont know when Cheryl’s Birthday is, But I Know that Benard does not know too!

Now, Albert is sure that Benard doesnt know. So in a way she is telling that the date is not 18 and 19. Because if it was 18 or 19, Benard knew the Date and month!

And Albert know this because she has been given a month which is not May or June. As only these months have dates possible 18, 19.

Thus Albert’s data left is:

Month               Possible dates

May                   15, 16, 19

June                  17, 18

July                   14, 16

Aug                   14, 15, 17

And what Benard knows:

Date                Possible Month

14                    July, Aug

15                    May, Aug

16                    May, July

17                    June, Aug

18                    June

19                     May

Now Benard would know Cheryl’s Birthday(now after Albert’s first statement)only if date given to him will be 15, 16 or 17.

Benard’s next statement is: At first I didnt knew when Cheryl’s Birthday is, But now I know!

Benards knows the Birthday!! So the date couldn’t be 14 as it has two months as possibilities!

Thus Albert’s data left is:

Month               Possible dates

May                   15, 16, 19

June                  17, 18

July                   14, 16

Aug                   14, 15, 17

And what Benard knows:

Date                Possible Month

14                    July, Aug

15                    May, Aug

16                    May, July

17                    June, Aug

18                    June

19                     May

Albert next says: Then I also know when is Cheryl’s Birthday!

Now look at Albert’s data. Albert will know the birthday only if the date is 16th!

Clearly the Month is July and Date is 16.

Cheryl was born on July 16!! 

P.S.: I’m sure the whole world will be looking for Cheryl’s on July 16 (with their own reasons ;))!!

Interesting right??

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