bhramarraj

Thanks Plasmid, you are absolutely right. I overlooked this. So I am again posting a modified solution, and awaiting valuable comments.

Sorry, I don't know why spoiler was not working

You said “B takes twice as long, so the escalator will have moved 20 steps,…..”

Kia, I have put your answer in terms of A, B, C, to make it clearer to me. So you go to the first one [A] and ask him "if I were to ask you 'is the second person is the random guy', would you say yes?" If the first person [A] is the truth teller, then it is easy, he would say ‘yes’ if the second person is the Random guy and ‘no’ if not. If the second person [i think it should be the first person ‘A’] is the liar and the second is the truth teller, then the liar [A] would have said ‘yes’ to ”is the second person is the random guy” but since he is still telling lies, he would say ‘no’. If the second person [i think first person ‘A’] is the liar and the second is the Random guy, then the liar would have said ‘no’ to “is the second person is the random guy' but since he is still telling lies, he would say ‘yes’. So in both cases, the truth teller and the liar would clearly indicate if the second guy was the Random guy. [Let me put it clearer: If A says ‘yes’ to the question asked, then B must be a Random guy; and if A says ‘no’ then B is not a Random guy.] Now what if the Random guy was the first person [A]? He would say ‘no’ if he was acting like a truth teller. And he would say ‘no’ if he was acting like the liar. So after the first question you know if the second guy is the Random guy or not. In more clear words If you hear ‘yes’ from the first guy [A], then second guy must be a Random guy and if you hear ‘no’ from the first guy [A], then second guy must not be a Random guy. If he is not, then you ask the second one a similar question, "if I were to ask you 'is the third person [C] is the random guy', would you say yes?" For the same reasons as above, after this question you know for sure who the random guy is. Now there is one more thing left, to find which one tell the truth and which one lies, and again, a similar question from the third person "if I were to ask you 'is the first person is the truth teller', would you say yes?" Or "If I were to ask you 'are you the truth teller', would you say yes?" And you know which one is which. The whole key is to ask a question. As I said, the trick to this puzzle is to force the liar into a double negative situation, and remember that the random guy either tells the truth or lies which would mean that the follows the same thinking patters as the liar. I hope that was clear. Kia, definitely it is clear, and I fully agree with you.

In that case one more trip i.e. 4 trips will be required to complete the task.

Hi David... ! is there any other simpler solution.......?

Sorry forgot to use spoiler.

let the age of three daughters be a, b, and c. Then according to the given conditions : a * b * c = 36 and a + b+ c = 13. There are two combinations possible: 1,6,6; 2,2,9; Then mother said that her oldest daughter was sleeping upstairs, which indicates she had only one daughter as oldest, so the combination 2,2,9 is correct.

y

In the original question it looks as if one train comes on the station at say 6:00 from left side, then another train comes from left side at 6:4.

Oh My.... I saw spoiler for typo error of Wolfgang after wards. Sorry the solution above is useless.

you are right....!

Here is my answer.