How many times per day does a 12hr clock's hands over lap?

[masraum]

Interesting!

It's a regular (old fashioned) clock that goes from 1-12.

How many times per day do the hour hand and minute hand overlap fully?

[Steve Carlton]

I'm thinking 24 looking at the question visually, but I'm not reconciling the fact that it takes 65 minutes each time for the minute hand to catch up to the hour hand. Final answer 24.

[red 928]

[masraum]

I'll add a note. If you count midnight at the beginning of the 24 hour period, then you shouldn't include midnight at the end (or vice versa). One day will only have one midnight, so whether you count the midnight at the beginning or end of the day, the other midnight belongs to the other day.

[dad911]

Originally Posted by Steve Carlton

I'm thinking 24 looking at the question visually, but I'm not reconciling the fact that it takes 65 minutes each time for the minute hand to catch up to the hour hand. Final answer 24.

Reconciling the fact..... overlap occurs every 65 minutes, not 60. 1440 (minutes per day) divided by 65(minutes per overlap) = 22 overlaps per day.

[Noah930]

Originally Posted by masraum

I'll add a note. If you count midnight at the beginning of the 24 hour period, then you shouldn't include midnight at the end (or vice versa). One day will only have one midnight, so whether you count the midnight at the beginning or end of the day, the other midnight belongs to the other day.

You need to put this up front, not on post #4. Because that changes my (and maybe others') answer.

[Seahawk]

23. Or not ^^^

1. time overlap occurs at 00:00:00
2. time overlap occurs at 01:05:27
3. time overlap occurs at 02:10:54
4. time overlap occurs at 03:16:21
5. time overlap occurs at 04:21:49
6. time overlap occurs at 05:27:16
7. time overlap occurs at 06:32:43
8. time overlap occurs at 07:38:10
9. time overlap occurs at 08:43:38
10. time overlap occurs at 09:49:05
11. time overlap occurs at 10:54:32
12. time overlap occurs at 12:00:00
13. time overlap occurs at 13:05:27
14. time overlap occurs at 14:10:54
15. time overlap occurs at 15:16:21
16. time overlap occurs at 16:21:49
17. time overlap occurs at 17:27:16
18. time overlap occurs at 18:32:43
19. time overlap occurs at 19:38:10
20. time overlap occurs at 20:43:38
21. time overlap occurs at 21:49:05
22. time overlap occurs at 22:54:32
23. time overlap occurs at 24:00:00 (since we count starting as one of overlaps, this might be excluded)

[Sooner or later]

22

You don't count the last (or first, your pick) 0/12/24. There are not three 0/12/24 o'clocks/hours in a 24 hour period.

[masraum]

Originally Posted by Seahawk

23. Or not ^^^

1. time overlap occurs at 00:00:00
2. time overlap occurs at 01:05:27
3. time overlap occurs at 02:10:54
4. time overlap occurs at 03:16:21
5. time overlap occurs at 04:21:49
6. time overlap occurs at 05:27:16
7. time overlap occurs at 06:32:43
8. time overlap occurs at 07:38:10
9. time overlap occurs at 08:43:38
10. time overlap occurs at 09:49:05
11. time overlap occurs at 10:54:32
12. time overlap occurs at 12:00:00
13. time overlap occurs at 13:05:27
14. time overlap occurs at 14:10:54
15. time overlap occurs at 15:16:21
16. time overlap occurs at 16:21:49
17. time overlap occurs at 17:27:16
18. time overlap occurs at 18:32:43
19. time overlap occurs at 19:38:10
20. time overlap occurs at 20:43:38
21. time overlap occurs at 21:49:05
22. time overlap occurs at 22:54:32
23. time overlap occurs at 24:00:00 (since we count starting as one of overlaps, this might be excluded)

Originally Posted by Sooner or later

22

You don't count the last (or first, your pick) 0/12/24. There are not three 0/12/24 o'clocks/hours in a 24 hour period.

Yep, These 2 answers combined very accurately give the answer.

If anyone wants to see the answer explained, including in a couple of more visual ways....

[Dixie]

The answer is indeed 22. I didn't post, because I didn't want to ruin it for others.

[masraum]

What I thought was interesting, a quick cursory thought would likely spawn the thought "once per hour except either the first or last won't count.

But there is NO overlap ever in the 11:00 - 11:59:59 hours (either one)

[masraum]

Originally Posted by Dixie

The answer is indeed 22. I didn't post, because I didn't want to ruin it for others.

That's because you're a smart cookie!

[WPOZZZ]

The correct answer is Zero. My clock is always blinking at 12:00

[Eric Hahl]

I get 24.

1. Midnight
2. 1:05am
3. 2:10
4. 3:15
5. 4:20
6. 5:25
7. 6:30
8. 7:35
9. 8:40
10. 9:45
11. 10:50
12. 11.55
13. Noon
14. 1:05pm
15. 2:10
16. 3:15
17. 4:20
18. 5:25
19. 6:30
20. 7:35
21. 8:40
22. 9:45
23. 10:50
24. 11.55pm

[masraum]

Originally Posted by Seahawk

1. time overlap occurs at 00:00:00
2. time overlap occurs at 01:05:27

Originally Posted by Eric Hahl

I get 24.

1. Midnight
2. 1:05am
3. 2:10
4. 3:15
5. 4:20
6. 5:25
7. 6:30
8. 7:35
9. 8:40
10. 9:45
11. 10:50
12. 11.55
13. Noon
14. 1:05pm
15. 2:10
16. 3:15
17. 4:20
18. 5:25
19. 6:30
20. 7:35
21. 8:40
22. 9:45
23. 10:50
24. 11.55pm

Seahawk's time is correct, it's 1:05:27 per hour, and that extra 27secs makes a difference. It's interesting that neither of thethe 11:00-11:59:59 hours has an overlap at all.

[john70t]

I guessed 22. The big hand rotates 24 times minus the small rotating twice and skipping ahead.

But that might be wrong, as start and stop are at the top.