"When is the train?"

Lonnie is taking the train to the Library. He tells Rosti the hour of his train’s departure and he tells Ann at which minute it leaves. He also tells them both that the train leaves between 0600 and 1000.

They consult the timetable and find the following services between those two time:

0632 0643 0650 0717 0746 0819 0832 0917 0919 0950
 
Rosti then says “I don’t know when Lonnie’s train leaves but i am sure that neither does Ann”

Ann Replies “I didn’t know his train, but now I do”

Rosti responds “Now I do as well!”

When is Lonnie’s train and how do you know?

THIS is how you should know the correct time!

Similar Kind of Puzzle! 

Scheduled Time of Lonnie's Train

What was the puzzle?

Lonnie tells Rosti the hour of his train’s departure and he tells Ann at which minute it leaves.

Rosti and Ann consult the timetable and find the following services between those two time: 

0632 0643 0650 0717 0746 0819 0832 0917 0919 0950

Rosti then says “I don’t know when Lonnie’s train leaves but i am sure that neither does Ann”

Ann Replies “I didn’t know his train, but now i do”

Rosti responds “Now I do as well!”

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1. If Ann had 43 as a number representing the minutes then she would have an idea of exact time of Lonnie's train as 0643 straightaway as 43 appears only once in the list.

But she says in her statement that she didn't know his train (initially). Hence, she must not had number 43.

2. Similarly, Ann must not had 46 as well as it appear only once in the list in form of 0746.

3. Now, let's think from Rosti's point of view for a moment. How he was sure that Ann too doesn't know the exact time.

Had he got number 6 (or 7) then what he would have thought - 

"Ann might have got 43 (or 46) and hence may know the exact time as 0643 (or 0646). Or she might not have the exact time if she has got any other number. 

I'm not sure whether Ann knows or doesn't know the exact time"

Since, Rosti is sure that Ann too doesn't know the exact time he must not have got number 6 or 7. 

So all timing with 6 and 7 hours in are eliminated leaving behind timing with 8 and 9 hours as - 

0819 0832 0917 0919 0950

4. Ann is smart enough to list out above timings as possible timings after Rosti's first statement.

Now if Ann had number 19 then she would have been confused with 2 timings 0819 and 0919. 

Since, she is sure that she has got correct time it must be among - 0832 0917 0950 where minutes are appearing uniquely.

5. What if Ann had got 17 (or 50) and she deduced correct time as 0917 (or 0950) ? 

That means Rosti must had number 9. With that number, how he would know the correct time whether it is 0917 or 0950?

Since, in his next statement he say that he too know the correct time he must have got number 8 and that's how he know the correct time is 0832.

And since Ann got number 32 with which she is sure that the correct time is 0832.