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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Route to Mumbai! Can you help the traveler? #trickyquestion #PGEE #twodoorsriddle

Hello Innovators!

Month of April is getting interesting with each week passing by with amazing mind boggling riddles! This month we did solve the reasoning problem of finding #cherylsbirthday. And just when the fun wasnt over, PGEE-15 gave the #twodoorsriddle problem as part of their GA section. They asked the riddle with a traveler who wishes to go to Mumbai. Lets see the complete problem statement…

A traveler wants to go Mumbai from Bengaluru. He decided to walk a certain road. Suddenly he meets a divergence in the road with two roads forking the road he was travelling. He knows for certain that one of these road goes to Delhi, while the other one goes to Mumbai. However he doesn’t know which is the correct one. He sees a small tea shop at the divergence. The tea shop is owned by identical twin brothers. There is no way you can differentiate between them by their physical appearance or by their voice. On reaching the tea shop, traveler finds out that one of these brothers always speak truth, while the other one always lies. But who speaks truth or lie is also unknown. Now the traveler’s dilemma is that he wants to find the route to Mumbai, but the twin brothers are as stubborn as the Genie in a bottle! And they give just one chance (unlike the Genie of Alladin who gives 3 wishes  😦 ). So the traveler can ask one question, and only one from any one of the brothers. What should he ask and to which brother? Can you help him?

P.S.Sorry, I added some masala to the story. Couldn’t resist… 😦

Tell us in the comments below what should the traveler do?

take me to solution