Clock puzzle

Re: Clock puzzle

I'm going to guess 7.5 degrees for question a. On questions b and c do the large hand and the small hand matter. In question a the large hand was the first encountered followed by the small hand. Is that what you are looking for in question b and c or is that irrelevant? If they are irrelevant I would guess that the answer to question c is 24 times. As for b my guess would be 8:45.

Re: Clock puzzle

Probably should have put a bit more thought into this, but I get 7.5° for the angle at 3:15. Another time with this angle would be at about 1.37 minutes after 12:00. Assuming a 12 hour clock, I would say this angle would appear 48 times in a 24 hour period.

Re: Clock puzzle

I get 22.5° at 8:45.

Re: Clock puzzle

Hi Don,

Can't sleep either, huh? Here was my thought process on 8:45. Big hand is on the 9 and small hand is 3/4 of the way through the hour. Since each hour represents 30 degrees, 1/4th of that is 7.5. Where did I go wrong?

Jim

Re: Clock puzzle

Hi Don,

I don't get the 48. If you think about the relationship between the small hand and the big hand it is going to form that specific angle once before the hour and once after the hour and hence the 24. Am I missing something?

Jim

Re: Clock puzzle

My bad. Sleep deprivation ;-) I was thinking of 9:45, not 8. Misread the post. ;-( Your answer to another time with the same angle is better than mine. More clear. I calculated the first instance that it would occur after midnight, which is when the hour hand is a bit over 8 degrees and the minute hand is around .7 degrees. (both rounded)

Re: Clock puzzle

The question said in a 24 hour period, which is twice around the dial. ;-) I agree on the twice an hour, it is just that it has to go around twice also, hence the 48.

Re: Clock puzzle

OOOHHHHHHH. You are right. Thank you.

Re: Clock puzzle

I got all three parts relatively quickly, as has the team here.

Unfortunately, I got two out of three.

Just like you guys!

Re: Clock puzzle

Looking for an exact time, not an approximate time. And remember the setting; no paper and pencil or calculator.

2 out of 3

My message was not clear. Just like you guys, I got

A) 7.5 degrees

B) 8:45

C) 48

Only two of those are correct.

Is this 3 out of 3

The answers are:

A. 0 degrees

B. 8:45

C. 24

With out a calculator to do the answer the off the top of the head answer would be zero degrees between the hands and it would occur once per hour or 24 times per day. In reality the alignment of the hands would not occur at exactly 3:15 but would be just before 3:17 and would also occur just before 8:47.

Lee

No :-(

2/3 of the ones I posted were correct, and you changed two, ending up with only 1/3 right. Your explanation tells why your A is not correct.

Re: Is this 3 out of 3

I am fairly sure that A and B are correct. If C is the incorrect one, then Maybe the answer to that one is 46. Got to think on it a bit more.

Re: No :-(

B) is an hour early

I don't think so

In fact, when it is 3:15, look at a clock with no numerals in the mirror, and it will look like it is 8:45.

Re: I don't think so

Opps, must be something like crossing the dateline on circumnavigation.

Re: 2 out of 3

C) 44

In a 12 hour period the minute hand crosses the hour hand 11 times.

We have a winner!

Yes, that is correct, and the easiest way to see the right answer. The minute hand goes around the face 24 times during the 24 hours, but the hour hand goes around 2 times in the same direction, so the minute hand only goes around 22 times relative to the hour hand.

But I still had a hard time seeing it in terms of the clock face until I looked at it like this: Look at the spaces between the hours. When the hour hand is between 1 and 2, between 2 and 3, ... or between 10 and 11, the minute hand can be 7.5 degrees on either side of the hour hand. But with the hour hand between 12 and 1, the minute hand cannot be 7.5 degrees behind the hour hand, and between 11 and 12, it can't be 7.5 degrees ahead of the hour hand.

44 was not an expected answer!!