Mixing
Mirrored clocks
Clash Royale CLAN TAG#URR8PPP
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Triangulating for the simplest puzzle that is still at least somewhat interesting to solve..
On the left side wall in this picture, we have two particular clocks:
1: an analog clock with identical hour and minute arms, and
2: a digital clock that shows initial zeroes when appropriate
During the course of a day, which of these clocks agrees more often with its horizontal mirror image?
visual geometry time
asked 2 hours ago
Bass
23.8k458153
 |Â
show 1 more comment
up vote
3
down vote
favorite
Triangulating for the simplest puzzle that is still at least somewhat interesting to solve..
On the left side wall in this picture, we have two particular clocks:
1: an analog clock with identical hour and minute arms, and
2: a digital clock that shows initial zeroes when appropriate
During the course of a day, which of these clocks agrees more often with its horizontal mirror image?
visual geometry time
asked 2 hours ago
Bass
23.8k458153
The right side is a vertical reflection of the left side no? I don't understand what you mean by horizontal mirror image in this case.
– Dorrulf
2 hours ago
In the image, hour and minute hands appear to be the same length. Are we to make this assumption for figuring out how many times they "match"?
– DqwertyC
2 hours ago
@DqwertyC he describes the analog clock as having identical hour and minute arms, so yes, I think that is the assumption you should make. IE: The minute hand on the left may be visually equal to the hour hand on the right, and that is acceptable.
– Dorrulf
2 hours ago
@Dorrulf That's what I get for diving into the question without reading it thoroughly :P
– DqwertyC
2 hours ago
@Dorrulf The picture is supposed to depict a horizontal reflection (over a vertical plane). If I'm still being unclear, please imagine that the right hand wall is a mirror; that is the intended meaning.
– Bass
2 hours ago
 |Â
show 1 more comment
up vote
3
down vote
favorite
up vote
3
down vote
favorite
Triangulating for the simplest puzzle that is still at least somewhat interesting to solve..
On the left side wall in this picture, we have two particular clocks:
1: an analog clock with identical hour and minute arms, and
2: a digital clock that shows initial zeroes when appropriate
During the course of a day, which of these clocks agrees more often with its horizontal mirror image?
visual geometry time
asked 2 hours ago
Bass
23.8k458153
Triangulating for the simplest puzzle that is still at least somewhat interesting to solve..
On the left side wall in this picture, we have two particular clocks:
1: an analog clock with identical hour and minute arms, and
2: a digital clock that shows initial zeroes when appropriate
During the course of a day, which of these clocks agrees more often with its horizontal mirror image?
visual geometry time
visual geometry time
asked 2 hours ago
Bass
23.8k458153
asked 2 hours ago
Bass
23.8k458153
asked 2 hours ago
Bass
23.8k458153
asked 2 hours ago
Bass
23.8k458153
asked 2 hours ago
Bass
23.8k458153
23.8k458153
The right side is a vertical reflection of the left side no? I don't understand what you mean by horizontal mirror image in this case.
– Dorrulf
2 hours ago
In the image, hour and minute hands appear to be the same length. Are we to make this assumption for figuring out how many times they "match"?
– DqwertyC
2 hours ago
@DqwertyC he describes the analog clock as having identical hour and minute arms, so yes, I think that is the assumption you should make. IE: The minute hand on the left may be visually equal to the hour hand on the right, and that is acceptable.
– Dorrulf
2 hours ago
@Dorrulf That's what I get for diving into the question without reading it thoroughly :P
– DqwertyC
2 hours ago
@Dorrulf The picture is supposed to depict a horizontal reflection (over a vertical plane). If I'm still being unclear, please imagine that the right hand wall is a mirror; that is the intended meaning.
– Bass
2 hours ago
 |Â
show 1 more comment
The right side is a vertical reflection of the left side no? I don't understand what you mean by horizontal mirror image in this case.
– Dorrulf
2 hours ago
In the image, hour and minute hands appear to be the same length. Are we to make this assumption for figuring out how many times they "match"?
– DqwertyC
2 hours ago
@DqwertyC he describes the analog clock as having identical hour and minute arms, so yes, I think that is the assumption you should make. IE: The minute hand on the left may be visually equal to the hour hand on the right, and that is acceptable.
– Dorrulf
2 hours ago
@Dorrulf That's what I get for diving into the question without reading it thoroughly :P
– DqwertyC
2 hours ago
@Dorrulf The picture is supposed to depict a horizontal reflection (over a vertical plane). If I'm still being unclear, please imagine that the right hand wall is a mirror; that is the intended meaning.
– Bass
2 hours ago
The right side is a vertical reflection of the left side no? I don't understand what you mean by horizontal mirror image in this case.
– Dorrulf
2 hours ago
The right side is a vertical reflection of the left side no? I don't understand what you mean by horizontal mirror image in this case.
– Dorrulf
2 hours ago
In the image, hour and minute hands appear to be the same length. Are we to make this assumption for figuring out how many times they "match"?
– DqwertyC
2 hours ago
In the image, hour and minute hands appear to be the same length. Are we to make this assumption for figuring out how many times they "match"?
– DqwertyC
2 hours ago
@DqwertyC he describes the analog clock as having identical hour and minute arms, so yes, I think that is the assumption you should make. IE: The minute hand on the left may be visually equal to the hour hand on the right, and that is acceptable.
– Dorrulf
2 hours ago
@DqwertyC he describes the analog clock as having identical hour and minute arms, so yes, I think that is the assumption you should make. IE: The minute hand on the left may be visually equal to the hour hand on the right, and that is acceptable.
– Dorrulf
2 hours ago
@Dorrulf That's what I get for diving into the question without reading it thoroughly :P
– DqwertyC
2 hours ago
@Dorrulf That's what I get for diving into the question without reading it thoroughly :P
– DqwertyC
2 hours ago
@Dorrulf The picture is supposed to depict a horizontal reflection (over a vertical plane). If I'm still being unclear, please imagine that the right hand wall is a mirror; that is the intended meaning.
– Bass
2 hours ago
@Dorrulf The picture is supposed to depict a horizontal reflection (over a vertical plane). If I'm still being unclear, please imagine that the right hand wall is a mirror; that is the intended meaning.
– Bass
2 hours ago
 |Â
show 1 more comment
4 Answers
4
active
oldest
votes
up vote
2
down vote
The times where the analog clock will match are
The same as the times that the analog clock has reflective symmetry across it's "y" axis. This will happen at least once an hour. The proof for this involves the Intermediate Value Theorem, but essentially boils down to the fact that, every hour, the hour hand continuously sweeps one part of the clock, while the minute hand continuously sweeps the entire clock. It follows that, in sweeping the entire clock, it must for an instant pass through the part of the clock that is currently opposite the hour hand.
It actually matches slightly more often than this, because they're already matching at noon/midnight, so it comes out to 13 matches every 12 hours, or 26 total.
The times where the digital clocks will match are
Again, where the clock has reflective symmetry across it's "y" axis (The colon). As @Dorrulf has already enumerated, this happens at 00:00, 02:50, 20:05, and 22:55. I'm not counting the times with ones in them, because they don't show up on the same half of the digit when reflected. This is a measly 4 total
So, it's clear that the reflections match more often for the
Analog Clock
answered 1 hour ago
DqwertyC
5,6571242
There is an additional match at 6:00 and 18:00 on analog clock since both handles are exactly on vertical axis.
– Phil1970
4 mins ago
add a comment |Â
up vote
0
down vote
Last try...
As a forward, I'm going more for the idea that the clocks read identical times rather than they just look similar.
The only analog positions I see matching would be at 12:30 and 3:45, and their self-reflections (6:00 and 9:15) for a total of 8 occurrences in 24-hr a day. (Thanks @ExcitedRaichu)
The digital clock has a few things of note beforehand:
The leading 0's and set to military time.
Again, if we function with the idea that as long as the times read the same (and the positions don't have to be exact - left oriented 1 versus right oriented 1), then we have these reflective cases: 0 to 0, 1 to 1, 2 to 5, 5 to 2. We can't use 8 because minutes only goes to 60. This gives us the following combinations (barring any were missed): 01:10, 11:11, 10:01, 15:21, 12:51, 05:20, 02:50. @DqwertC also found: 00:00, 02:50, 20:05, and 22:55.
That puts us at a ration of 8:11, in favor of the digital clock.
answered 2 hours ago
Dorrulf
4265
I'm still unsure of my understanding of "reflective agreement" though xD
– Dorrulf
2 hours ago
doesn’t (rot13) fvkbpybpx work for analog as well?
– Excited Raichu
2 hours ago
Also, most digital clocks don’t have an 0 in front of the hour number if it’s one digit
– Excited Raichu
2 hours ago
1
@ExcitedRaichu It explicitly says they do in the problem.
– DqwertyC
2 hours ago
@DqwertC whoops. missed that.
– Excited Raichu
2 hours ago
add a comment |Â
up vote
0
down vote
Assuming 'agrees with' is synonymous with 'looks the same'...
Analog
As suggested by DqwertyC, the analogue clock will agree 26 times in 24 hours if you include both mid-nights. If you argue that there is only one midnight in a 24 hour day then this can be reduced to 25 times. Assuming the latter these times are approximately: 00:55, 1:50, 2:46, 3:41, 4:37, 5:32, 6:28, 7:22, 8:18, 9:14, 10:09, 11:04, and 12:00 plus the equivalent times in the afternoon.
Digital
As suggested by Dorrulf and DqwertyC there are a minimum of 4 times when the digital clocks agree (if only (2|5), and (0|0) digits are considered to be mirror images, and a maximum of 11 times if (1|1) is also included.
Conclusion
Either way, 12 (or 13) trumps 11 (or 4), so the analog clock wins.
answered 48 mins ago
Penguino
6,7921866
You need to include one midnight and one noon so 26 is correct. With 2 midnight, it would be 27! Also there are 2 extra matches at 6:00 and 18:00.
– Phil1970
2 mins ago
add a comment |Â
up vote
0
down vote
Analog clock matches are:
One math per ~55 minutes = 13 matches
An additional match at 6:00 = 1 match
Those matches occurs twice per day since the hour handle makes 2 complete turns by day.
(13 + 1) × 2 = 28 matches.
For the digital clock we have:
The following symmetries : 0 <--> 0, 1 <--> 1, 2 <--> 5 and 8 <--> 8
Starting at midnight, we have:
Leading 0: 00:00, 01:10, 02:50, 05:20 = 4 matches
Leading 1: 10:01, 11:11, 12:50, 15:20 = 4 matches
Leading 2: 20:05, 21:15, 22:55 = 3 matches
Leading 5: No matches
Leading 8: No matches
Thus we have 11 matches per day
So the result is:
The analog clock matches more often.
answered 20 mins ago
Phil1970
1993
New contributor
Phil1970 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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4 Answers
4
active
oldest
votes
4 Answers
4
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
The times where the analog clock will match are
The same as the times that the analog clock has reflective symmetry across it's "y" axis. This will happen at least once an hour. The proof for this involves the Intermediate Value Theorem, but essentially boils down to the fact that, every hour, the hour hand continuously sweeps one part of the clock, while the minute hand continuously sweeps the entire clock. It follows that, in sweeping the entire clock, it must for an instant pass through the part of the clock that is currently opposite the hour hand.
It actually matches slightly more often than this, because they're already matching at noon/midnight, so it comes out to 13 matches every 12 hours, or 26 total.
The times where the digital clocks will match are
Again, where the clock has reflective symmetry across it's "y" axis (The colon). As @Dorrulf has already enumerated, this happens at 00:00, 02:50, 20:05, and 22:55. I'm not counting the times with ones in them, because they don't show up on the same half of the digit when reflected. This is a measly 4 total
So, it's clear that the reflections match more often for the
Analog Clock
answered 1 hour ago
DqwertyC
5,6571242
There is an additional match at 6:00 and 18:00 on analog clock since both handles are exactly on vertical axis.
– Phil1970
4 mins ago
add a comment |Â
up vote
2
down vote
The times where the analog clock will match are
The same as the times that the analog clock has reflective symmetry across it's "y" axis. This will happen at least once an hour. The proof for this involves the Intermediate Value Theorem, but essentially boils down to the fact that, every hour, the hour hand continuously sweeps one part of the clock, while the minute hand continuously sweeps the entire clock. It follows that, in sweeping the entire clock, it must for an instant pass through the part of the clock that is currently opposite the hour hand.
It actually matches slightly more often than this, because they're already matching at noon/midnight, so it comes out to 13 matches every 12 hours, or 26 total.
The times where the digital clocks will match are
Again, where the clock has reflective symmetry across it's "y" axis (The colon). As @Dorrulf has already enumerated, this happens at 00:00, 02:50, 20:05, and 22:55. I'm not counting the times with ones in them, because they don't show up on the same half of the digit when reflected. This is a measly 4 total
So, it's clear that the reflections match more often for the
Analog Clock
answered 1 hour ago
DqwertyC
5,6571242
There is an additional match at 6:00 and 18:00 on analog clock since both handles are exactly on vertical axis.
– Phil1970
4 mins ago
add a comment |Â
up vote
2
down vote
up vote
2
down vote
The times where the analog clock will match are
The same as the times that the analog clock has reflective symmetry across it's "y" axis. This will happen at least once an hour. The proof for this involves the Intermediate Value Theorem, but essentially boils down to the fact that, every hour, the hour hand continuously sweeps one part of the clock, while the minute hand continuously sweeps the entire clock. It follows that, in sweeping the entire clock, it must for an instant pass through the part of the clock that is currently opposite the hour hand.
It actually matches slightly more often than this, because they're already matching at noon/midnight, so it comes out to 13 matches every 12 hours, or 26 total.
The times where the digital clocks will match are
Again, where the clock has reflective symmetry across it's "y" axis (The colon). As @Dorrulf has already enumerated, this happens at 00:00, 02:50, 20:05, and 22:55. I'm not counting the times with ones in them, because they don't show up on the same half of the digit when reflected. This is a measly 4 total
So, it's clear that the reflections match more often for the
Analog Clock
answered 1 hour ago
DqwertyC
5,6571242
The times where the analog clock will match are
The same as the times that the analog clock has reflective symmetry across it's "y" axis. This will happen at least once an hour. The proof for this involves the Intermediate Value Theorem, but essentially boils down to the fact that, every hour, the hour hand continuously sweeps one part of the clock, while the minute hand continuously sweeps the entire clock. It follows that, in sweeping the entire clock, it must for an instant pass through the part of the clock that is currently opposite the hour hand.
It actually matches slightly more often than this, because they're already matching at noon/midnight, so it comes out to 13 matches every 12 hours, or 26 total.
The times where the digital clocks will match are
Again, where the clock has reflective symmetry across it's "y" axis (The colon). As @Dorrulf has already enumerated, this happens at 00:00, 02:50, 20:05, and 22:55. I'm not counting the times with ones in them, because they don't show up on the same half of the digit when reflected. This is a measly 4 total
So, it's clear that the reflections match more often for the
Analog Clock
answered 1 hour ago
DqwertyC
5,6571242
answered 1 hour ago
DqwertyC
5,6571242
answered 1 hour ago
DqwertyC
5,6571242
answered 1 hour ago
DqwertyC
5,6571242
5,6571242
There is an additional match at 6:00 and 18:00 on analog clock since both handles are exactly on vertical axis.
– Phil1970
4 mins ago
add a comment |Â
There is an additional match at 6:00 and 18:00 on analog clock since both handles are exactly on vertical axis.
– Phil1970
4 mins ago
There is an additional match at 6:00 and 18:00 on analog clock since both handles are exactly on vertical axis.
– Phil1970
4 mins ago
There is an additional match at 6:00 and 18:00 on analog clock since both handles are exactly on vertical axis.
– Phil1970
4 mins ago
add a comment |Â
up vote
0
down vote
Last try...
As a forward, I'm going more for the idea that the clocks read identical times rather than they just look similar.
The only analog positions I see matching would be at 12:30 and 3:45, and their self-reflections (6:00 and 9:15) for a total of 8 occurrences in 24-hr a day. (Thanks @ExcitedRaichu)
The digital clock has a few things of note beforehand:
The leading 0's and set to military time.
Again, if we function with the idea that as long as the times read the same (and the positions don't have to be exact - left oriented 1 versus right oriented 1), then we have these reflective cases: 0 to 0, 1 to 1, 2 to 5, 5 to 2. We can't use 8 because minutes only goes to 60. This gives us the following combinations (barring any were missed): 01:10, 11:11, 10:01, 15:21, 12:51, 05:20, 02:50. @DqwertC also found: 00:00, 02:50, 20:05, and 22:55.
That puts us at a ration of 8:11, in favor of the digital clock.
answered 2 hours ago
Dorrulf
4265
I'm still unsure of my understanding of "reflective agreement" though xD
– Dorrulf
2 hours ago
doesn’t (rot13) fvkbpybpx work for analog as well?
– Excited Raichu
2 hours ago
Also, most digital clocks don’t have an 0 in front of the hour number if it’s one digit
– Excited Raichu
2 hours ago
1
@ExcitedRaichu It explicitly says they do in the problem.
– DqwertyC
2 hours ago
@DqwertC whoops. missed that.
– Excited Raichu
2 hours ago
add a comment |Â
up vote
0
down vote
Last try...
As a forward, I'm going more for the idea that the clocks read identical times rather than they just look similar.
The only analog positions I see matching would be at 12:30 and 3:45, and their self-reflections (6:00 and 9:15) for a total of 8 occurrences in 24-hr a day. (Thanks @ExcitedRaichu)
The digital clock has a few things of note beforehand:
The leading 0's and set to military time.
Again, if we function with the idea that as long as the times read the same (and the positions don't have to be exact - left oriented 1 versus right oriented 1), then we have these reflective cases: 0 to 0, 1 to 1, 2 to 5, 5 to 2. We can't use 8 because minutes only goes to 60. This gives us the following combinations (barring any were missed): 01:10, 11:11, 10:01, 15:21, 12:51, 05:20, 02:50. @DqwertC also found: 00:00, 02:50, 20:05, and 22:55.
That puts us at a ration of 8:11, in favor of the digital clock.
answered 2 hours ago
Dorrulf
4265
I'm still unsure of my understanding of "reflective agreement" though xD
– Dorrulf
2 hours ago
doesn’t (rot13) fvkbpybpx work for analog as well?
– Excited Raichu
2 hours ago
Also, most digital clocks don’t have an 0 in front of the hour number if it’s one digit
– Excited Raichu
2 hours ago
1
@ExcitedRaichu It explicitly says they do in the problem.
– DqwertyC
2 hours ago
@DqwertC whoops. missed that.
– Excited Raichu
2 hours ago
add a comment |Â
up vote
0
down vote
up vote
0
down vote
Last try...
As a forward, I'm going more for the idea that the clocks read identical times rather than they just look similar.
The only analog positions I see matching would be at 12:30 and 3:45, and their self-reflections (6:00 and 9:15) for a total of 8 occurrences in 24-hr a day. (Thanks @ExcitedRaichu)
The digital clock has a few things of note beforehand:
The leading 0's and set to military time.
Again, if we function with the idea that as long as the times read the same (and the positions don't have to be exact - left oriented 1 versus right oriented 1), then we have these reflective cases: 0 to 0, 1 to 1, 2 to 5, 5 to 2. We can't use 8 because minutes only goes to 60. This gives us the following combinations (barring any were missed): 01:10, 11:11, 10:01, 15:21, 12:51, 05:20, 02:50. @DqwertC also found: 00:00, 02:50, 20:05, and 22:55.
That puts us at a ration of 8:11, in favor of the digital clock.
answered 2 hours ago
Dorrulf
4265
Last try...
As a forward, I'm going more for the idea that the clocks read identical times rather than they just look similar.
The only analog positions I see matching would be at 12:30 and 3:45, and their self-reflections (6:00 and 9:15) for a total of 8 occurrences in 24-hr a day. (Thanks @ExcitedRaichu)
The digital clock has a few things of note beforehand:
The leading 0's and set to military time.
Again, if we function with the idea that as long as the times read the same (and the positions don't have to be exact - left oriented 1 versus right oriented 1), then we have these reflective cases: 0 to 0, 1 to 1, 2 to 5, 5 to 2. We can't use 8 because minutes only goes to 60. This gives us the following combinations (barring any were missed): 01:10, 11:11, 10:01, 15:21, 12:51, 05:20, 02:50. @DqwertC also found: 00:00, 02:50, 20:05, and 22:55.
That puts us at a ration of 8:11, in favor of the digital clock.
answered 2 hours ago
Dorrulf
4265
edited 1 hour ago
answered 2 hours ago
Dorrulf
4265
answered 2 hours ago
Dorrulf
4265
answered 2 hours ago
Dorrulf
4265
4265
I'm still unsure of my understanding of "reflective agreement" though xD
– Dorrulf
2 hours ago
doesn’t (rot13) fvkbpybpx work for analog as well?
– Excited Raichu
2 hours ago
Also, most digital clocks don’t have an 0 in front of the hour number if it’s one digit
– Excited Raichu
2 hours ago
1
@ExcitedRaichu It explicitly says they do in the problem.
– DqwertyC
2 hours ago
@DqwertC whoops. missed that.
– Excited Raichu
2 hours ago
add a comment |Â
I'm still unsure of my understanding of "reflective agreement" though xD
– Dorrulf
2 hours ago
doesn’t (rot13) fvkbpybpx work for analog as well?
– Excited Raichu
2 hours ago
Also, most digital clocks don’t have an 0 in front of the hour number if it’s one digit
– Excited Raichu
2 hours ago
1
@ExcitedRaichu It explicitly says they do in the problem.
– DqwertyC
2 hours ago
@DqwertC whoops. missed that.
– Excited Raichu
2 hours ago
I'm still unsure of my understanding of "reflective agreement" though xD
– Dorrulf
2 hours ago
I'm still unsure of my understanding of "reflective agreement" though xD
– Dorrulf
2 hours ago
doesn’t (rot13) fvkbpybpx work for analog as well?
– Excited Raichu
2 hours ago
doesn’t (rot13) fvkbpybpx work for analog as well?
– Excited Raichu
2 hours ago
Also, most digital clocks don’t have an 0 in front of the hour number if it’s one digit
– Excited Raichu
2 hours ago
Also, most digital clocks don’t have an 0 in front of the hour number if it’s one digit
– Excited Raichu
2 hours ago
1
1
@ExcitedRaichu It explicitly says they do in the problem.
– DqwertyC
2 hours ago
@ExcitedRaichu It explicitly says they do in the problem.
– DqwertyC
2 hours ago
@DqwertC whoops. missed that.
– Excited Raichu
2 hours ago
@DqwertC whoops. missed that.
– Excited Raichu
2 hours ago
add a comment |Â
up vote
0
down vote
Assuming 'agrees with' is synonymous with 'looks the same'...
Analog
As suggested by DqwertyC, the analogue clock will agree 26 times in 24 hours if you include both mid-nights. If you argue that there is only one midnight in a 24 hour day then this can be reduced to 25 times. Assuming the latter these times are approximately: 00:55, 1:50, 2:46, 3:41, 4:37, 5:32, 6:28, 7:22, 8:18, 9:14, 10:09, 11:04, and 12:00 plus the equivalent times in the afternoon.
Digital
As suggested by Dorrulf and DqwertyC there are a minimum of 4 times when the digital clocks agree (if only (2|5), and (0|0) digits are considered to be mirror images, and a maximum of 11 times if (1|1) is also included.
Conclusion
Either way, 12 (or 13) trumps 11 (or 4), so the analog clock wins.
answered 48 mins ago
Penguino
6,7921866
You need to include one midnight and one noon so 26 is correct. With 2 midnight, it would be 27! Also there are 2 extra matches at 6:00 and 18:00.
– Phil1970
2 mins ago
add a comment |Â
up vote
0
down vote
Assuming 'agrees with' is synonymous with 'looks the same'...
Analog
As suggested by DqwertyC, the analogue clock will agree 26 times in 24 hours if you include both mid-nights. If you argue that there is only one midnight in a 24 hour day then this can be reduced to 25 times. Assuming the latter these times are approximately: 00:55, 1:50, 2:46, 3:41, 4:37, 5:32, 6:28, 7:22, 8:18, 9:14, 10:09, 11:04, and 12:00 plus the equivalent times in the afternoon.
Digital
As suggested by Dorrulf and DqwertyC there are a minimum of 4 times when the digital clocks agree (if only (2|5), and (0|0) digits are considered to be mirror images, and a maximum of 11 times if (1|1) is also included.
Conclusion
Either way, 12 (or 13) trumps 11 (or 4), so the analog clock wins.
answered 48 mins ago
Penguino
6,7921866
You need to include one midnight and one noon so 26 is correct. With 2 midnight, it would be 27! Also there are 2 extra matches at 6:00 and 18:00.
– Phil1970
2 mins ago
add a comment |Â
up vote
0
down vote
up vote
0
down vote
Assuming 'agrees with' is synonymous with 'looks the same'...
Analog
As suggested by DqwertyC, the analogue clock will agree 26 times in 24 hours if you include both mid-nights. If you argue that there is only one midnight in a 24 hour day then this can be reduced to 25 times. Assuming the latter these times are approximately: 00:55, 1:50, 2:46, 3:41, 4:37, 5:32, 6:28, 7:22, 8:18, 9:14, 10:09, 11:04, and 12:00 plus the equivalent times in the afternoon.
Digital
As suggested by Dorrulf and DqwertyC there are a minimum of 4 times when the digital clocks agree (if only (2|5), and (0|0) digits are considered to be mirror images, and a maximum of 11 times if (1|1) is also included.
Conclusion
Either way, 12 (or 13) trumps 11 (or 4), so the analog clock wins.
answered 48 mins ago
Penguino
6,7921866
Assuming 'agrees with' is synonymous with 'looks the same'...
Analog
As suggested by DqwertyC, the analogue clock will agree 26 times in 24 hours if you include both mid-nights. If you argue that there is only one midnight in a 24 hour day then this can be reduced to 25 times. Assuming the latter these times are approximately: 00:55, 1:50, 2:46, 3:41, 4:37, 5:32, 6:28, 7:22, 8:18, 9:14, 10:09, 11:04, and 12:00 plus the equivalent times in the afternoon.
Digital
As suggested by Dorrulf and DqwertyC there are a minimum of 4 times when the digital clocks agree (if only (2|5), and (0|0) digits are considered to be mirror images, and a maximum of 11 times if (1|1) is also included.
Conclusion
Either way, 12 (or 13) trumps 11 (or 4), so the analog clock wins.
answered 48 mins ago
Penguino
6,7921866
answered 48 mins ago
Penguino
6,7921866
answered 48 mins ago
Penguino
6,7921866
answered 48 mins ago
Penguino
6,7921866
6,7921866
You need to include one midnight and one noon so 26 is correct. With 2 midnight, it would be 27! Also there are 2 extra matches at 6:00 and 18:00.
– Phil1970
2 mins ago
add a comment |Â
You need to include one midnight and one noon so 26 is correct. With 2 midnight, it would be 27! Also there are 2 extra matches at 6:00 and 18:00.
– Phil1970
2 mins ago
You need to include one midnight and one noon so 26 is correct. With 2 midnight, it would be 27! Also there are 2 extra matches at 6:00 and 18:00.
– Phil1970
2 mins ago
You need to include one midnight and one noon so 26 is correct. With 2 midnight, it would be 27! Also there are 2 extra matches at 6:00 and 18:00.
– Phil1970
2 mins ago
add a comment |Â
up vote
0
down vote
Analog clock matches are:
One math per ~55 minutes = 13 matches
An additional match at 6:00 = 1 match
Those matches occurs twice per day since the hour handle makes 2 complete turns by day.
(13 + 1) × 2 = 28 matches.
For the digital clock we have:
The following symmetries : 0 <--> 0, 1 <--> 1, 2 <--> 5 and 8 <--> 8
Starting at midnight, we have:
Leading 0: 00:00, 01:10, 02:50, 05:20 = 4 matches
Leading 1: 10:01, 11:11, 12:50, 15:20 = 4 matches
Leading 2: 20:05, 21:15, 22:55 = 3 matches
Leading 5: No matches
Leading 8: No matches
Thus we have 11 matches per day
So the result is:
The analog clock matches more often.
answered 20 mins ago
Phil1970
1993
New contributor
Phil1970 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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add a comment |Â
up vote
0
down vote
Analog clock matches are:
One math per ~55 minutes = 13 matches
An additional match at 6:00 = 1 match
Those matches occurs twice per day since the hour handle makes 2 complete turns by day.
(13 + 1) × 2 = 28 matches.
For the digital clock we have:
The following symmetries : 0 <--> 0, 1 <--> 1, 2 <--> 5 and 8 <--> 8
Starting at midnight, we have:
Leading 0: 00:00, 01:10, 02:50, 05:20 = 4 matches
Leading 1: 10:01, 11:11, 12:50, 15:20 = 4 matches
Leading 2: 20:05, 21:15, 22:55 = 3 matches
Leading 5: No matches
Leading 8: No matches
Thus we have 11 matches per day
So the result is:
The analog clock matches more often.
answered 20 mins ago
Phil1970
1993
New contributor
Phil1970 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |Â
up vote
0
down vote
up vote
0
down vote
Analog clock matches are:
One math per ~55 minutes = 13 matches
An additional match at 6:00 = 1 match
Those matches occurs twice per day since the hour handle makes 2 complete turns by day.
(13 + 1) × 2 = 28 matches.
For the digital clock we have:
The following symmetries : 0 <--> 0, 1 <--> 1, 2 <--> 5 and 8 <--> 8
Starting at midnight, we have:
Leading 0: 00:00, 01:10, 02:50, 05:20 = 4 matches
Leading 1: 10:01, 11:11, 12:50, 15:20 = 4 matches
Leading 2: 20:05, 21:15, 22:55 = 3 matches
Leading 5: No matches
Leading 8: No matches
Thus we have 11 matches per day
So the result is:
The analog clock matches more often.
answered 20 mins ago
Phil1970
1993
New contributor
Phil1970 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Analog clock matches are:
One math per ~55 minutes = 13 matches
An additional match at 6:00 = 1 match
Those matches occurs twice per day since the hour handle makes 2 complete turns by day.
(13 + 1) × 2 = 28 matches.
For the digital clock we have:
The following symmetries : 0 <--> 0, 1 <--> 1, 2 <--> 5 and 8 <--> 8
Starting at midnight, we have:
Leading 0: 00:00, 01:10, 02:50, 05:20 = 4 matches
Leading 1: 10:01, 11:11, 12:50, 15:20 = 4 matches
Leading 2: 20:05, 21:15, 22:55 = 3 matches
Leading 5: No matches
Leading 8: No matches
Thus we have 11 matches per day
So the result is:
The analog clock matches more often.
answered 20 mins ago
Phil1970
1993
New contributor
Phil1970 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 7 mins ago
answered 20 mins ago
Phil1970
1993
New contributor
Phil1970 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered 20 mins ago
Phil1970
1993
answered 20 mins ago
Phil1970
1993
1993
New contributor
Phil1970 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Phil1970 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Phil1970 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |Â
add a comment |Â
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The right side is a vertical reflection of the left side no? I don't understand what you mean by horizontal mirror image in this case.
– Dorrulf
2 hours ago
In the image, hour and minute hands appear to be the same length. Are we to make this assumption for figuring out how many times they "match"?
– DqwertyC
2 hours ago
@DqwertyC he describes the analog clock as having identical hour and minute arms, so yes, I think that is the assumption you should make. IE: The minute hand on the left may be visually equal to the hour hand on the right, and that is acceptable.
– Dorrulf
2 hours ago
@Dorrulf That's what I get for diving into the question without reading it thoroughly :P
– DqwertyC
2 hours ago
@Dorrulf The picture is supposed to depict a horizontal reflection (over a vertical plane). If I'm still being unclear, please imagine that the right hand wall is a mirror; that is the intended meaning.
– Bass
2 hours ago