On one of his trips to Switzerland Professor Egghead bought a handcrafted cuckoo clock that chimes on every hour and half hour mark. On whole hour marks the little birdie cuckoos once for each hour, and on half hour marks it cuckoos only once.

One night our favorite professor was wakened suddenly and realized that the clock had chimed but he did not know how many times. As he lay awake thinking about nothing in particular he heard the birdie cuckoo once and he started to wonder what time it was.

What is the longest amount of time Professor Egghead would have to lie awake before he knew for sure what time it was?

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## Thursday, February 28, 2008

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## 7 comments:

Time from right after awaken to right before the next hour mark is:

30mins - time for one-cuckoo soundLongest time to know for sure what time it were is:

time for the whole 12-cuckoo soundThe total time is:

30mins - time for the 11-cuckoo soundExample: if each cuckoo is chimed after another for 1sec, the total time is 30mins - (11secs-1sec) = 29mins and 50secs

the longest time he would have to wait is 1 hour. This is if the cuckoo chimed once because it was 1 am.

In any other case it would be the half hour mark. So he would have to wait 30 minutes.

Longest time to wait and the answer is 1 hour.

If you want to be all 'mathy', 30 minutes would be the correct answer: 30 minutes after the 1 cuckoo he would hear either multiple cuckoos and know the hour. If at that time he once again hears only 1 cuckoo that means it is 1:30.

Alternatively, the longest amount of time he'll have to wait is equal to the amount of time it would take him to haul his lazy butt out of bed to go read the clockface. :D

1 hour ...

12:30 it chimes once

1:00 it chimes once. At this point it could either be 1:00 or 1:30 ... so he'd have to wait another half hour to know for sure.

2 hours. If it was the 12:00 chime he missed, he would have to wait till 2:oo to hear other than one chime.

The time would be 1.5 hours. If he woke up at 12, and he heard 3 single chimes in a row, he would know that it is 1:30.

1 hour from cookoo call he was awake for and 1.5 hours from cookoo that awoke him

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