Solution to Route To Mumbai Problem! #PGEE #trickyquestion #twodoorsriddle


Lets have a look at the constraints of the problem…

1) One of the two roads go to Mumbai – the traveler’s destination.

2) One of the two brothers speak truth and other is a liar.

If the traveler asks the direct question to one of the brothers- “Which road goes to Mumbai?” to any one of the brothers, there could be one of the two cases:

  • The traveler asked this question to the brother who speaks truth. And he is pointing to the right road.
  • The traveler asked this question to the brother who speaks lie. And he is pointing to the wrong road.

In any of the case, the traveler is in 50% probability of getting the right road. Since there is no way traveler can tell with this question who is the truth telling brother. Clearly direct question is no way to our solution.

But if we think little logically and ask the traveler this question to one of the brothers – “What do you think if I asked your brother(means the other brother) on which road goes to Mumbai, what will be his reply?”

Now lets look at the possible answers to this question. Any one of the two cases are possible –

  • Traveler asked this question from  the Truth telling brother. Now the truth telling brother always speaks truth. And he know that his brother is a liar. So he must reply the road his brother will point to, on asking the route to Mumbai. Since his brother is a liar, He will point to the Road that leads to Delhi. Truth speaking brother will thus point to road to Delhi as his reply to the intelligent question asked.
  • Traveler asked this question from the liar brother. Now he knows that his brother is truth speaking person. And his brother will point to Route to Mumbai on the question – Which road goes to Mumbai. But here comes the Twist! This brother is a liar. He always speak false. So he will point to route to Delhi as opposed to his brother’s reply. 

Notice the situation carefully. In both cases the traveler is getting pointed towards the Route to Delhi. Now this traveler is smart. And he had already analyzed the responses before asking his intelligent question. So he will now know which road is wrong. Clearly the other one is his Route to Mumbai!

Happy travelling Sir!


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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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