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

Answer 2

Steve's bus is at 08: 32.

• Alice does not know the bus timing since each hour has more than 1 timing .

• Also, Alice says Annie also does not know the timing.

• If it was 6 hr, then at 43 minutes, Annie would have known that 6: 43 was the bus timing.

• Therefore 6 is not the correct hour, hence cancelled out.

• If it was 7 hour, then at 46 minutes, Annie would know that the timing was 7 : 46.

• Therefore 7 is also not the correct hour, hence cancelled out.

• If it was 8 hour, then Annie could not know the exact time as 19 & 32 minutes were available in the same hour which is 8.

• Therefore 8 is also not the correct hour, hence cancelled out.

• If it was 9 hour, Annie could not know the exact time as 17, 19 & 50 minutes were again available in the same hour that is 9.

• Therefore 9 is not the correct hour as well, hence cancelled out.

• Now, Annie knows that the hour is either 8 or 9.

• 19 is common in both 8 and 9, hence, minute can not be 19.

• Thus, bus timing can be either 8 : 32 , 9:17 or 9: 50.

• Alice says that she also knows the bus timing .

• As in case of 9 hour, there are more than one options available. Thus, if it has been 9 hour , it was not possible for Alice to have known the exact timing .

• Henceforth, it must be 8: 32

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