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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