Question

Steve is taking a bus to Central Park. Steve tells Alice the hour of his bus departure and he tells Annie at which minute it leaves. He also tells them both that the bus leaves between 0600 and 1000.

Alice & Annie consult the timetable and find the following services between those two time: 0632 0643 0650 0717 0746 0819 0832 0917 0919 0950.

Alice then says “I don’t know when Steve’s bus leaves but I am sure that neither does Annie”

Annie Replies “I didn’t know his bus, but now i do”

Alice responds “Now I do as well!”

When is Steve’s bus?​

Answer 1

Answer:

0832

Explanation:

When Alice is sure that Annie doesn’t know the time the options of 06 and 07 can be removed...if it’s in the options of 06 or 07 Alice would have had a doubt that Annie knows the answer as 43 and 46 are not repeated

Annie knows that it’s not 06 07 So she has 0819 0832 0917 0919 0950...if its 19 minutes Annie would have had a doubt in 0819 and 0919 so remove then

0832 0917 0950 are left

As soon as Annie knows the time Alice knows it as well...if it’s in 09 Alice would have had a doubt in 0917 and 0950....so it’s 0832

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Answer 2

Answer is 8:32

Step-by-step explanation:

• Alice says “I don’t know when Steve’s bus leaves but neither does Annie”
• Annie conveys the idea that she knows she has a minute.
• Otherwise, she would figure out without Alice knowing hence all hours with 6 and 7 are ruled out.
• After that she makes it clear that she knows the answer by saying that “I didn’t know before but now I do”                                                  
• So we are left with 8:32, 9:17 and 9:50
• Later when Alice confirms that since there is only one time is of the 8th hour and she is confident she knows hence the answer is 8:32.