Ron and Tim works for Sara. Sara told them that her sister Maya will be passing through the town subway between 17:00 and 21:00 hours and asked them to hand over a parcel to her sister when she arrives at the subway junction. She tells the hour of her sister's arrival to Ron and minutes of her arrival to Tim.
Ron and Tim find the subway Time-table and got to know the arrival trains timing between 17:00 and 21:00 hours as follows: 17:22 17:29 17:45 18:06 18:28 19:08 19:22 20:06 20:08 20:45.
After both looked at the time-table :-
Ron tells to Tim:- "I do not know what time Maya will be coming and I am sure that neither you know"
Tim replies:- "I didn't knew Maya's train time, but now I know"
Ron replies:- "Now I know as well"
What is Maya's train timing.
Answers
Given:
Train passing time between 17:00 and 21:00
Time duration - 17:22 17:29 17:45 18:06 18:28 19:08 19:22 20:06 20:08 20:45.
To Find:
Maya's train timing.
Solution:
At 17 hour - - - 22 - 29 45
At 18 hour 06 - - 28 -
At 19 hour - 08 22 - - -
At 20 hour 06 08 - - - 45
In the given hours 28 and 29 minutes are unique and appear only once
Ron just knows the hour and she does not know the precise time of the subway. But she also says that Tim doesn't know minutes, so the hour Ron knows has no special timing.
Thus, hour must be 19 or 20
Since, Tim knows that hour is 19 or 20 hence minutes can not be 8 otherwise she would not know exact timing, thus we are left with 3 timings which are 19:22 20:06 20:45
Now, Ron also knows the time so the hour is 19 and that has only one time, Anser: Maya train timing is 19 : 22