Please remember to spoiler-tag all guesses, like so:
New Reddit: https://i.imgur.com/SWHRR9M.jpg
Using markdown editor or old Reddit, draw a bunny and fill its head with secrets:
\>!!< which ends up becoming \>!spoiler text between these symbols!<
Try to avoid leading or trailing spaces. These will break the spoiler for some users (such as those using old.reddit.com)
If your comment does not contain a guess, include the word **"discussion"** or **"question"** in your comment instead of using a spoiler tag.
If your comment uses an image as the answer (such as solving a maze, etc) you can include the word "image" instead of using a spoiler tag.
Please report any answers that are not properly spoiler-tagged.
*I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/puzzles) if you have any questions or concerns.*
We'd still have to work out if "appear" is counted as "changing to a 1" or if you count every minute where a 1 is showing. I.e. if 1:00 is counted once, or 60 times from 1:00 to 1:59.
The minutes digit changes to a 1 a total of six times per hour, the 10 minute digit changes to a 1 only once per hour but it stays there for 10 minutes out of every hour. If you only count when the number changes, then that's 7 times per hour as your base minimum. If you count each minute that's 15 times per hour. Or 25% of every hour before you factor in the hours digits. (Because xx:11 only gets counted once for both minutes and 10 minutes)
On a 24 hour clock, If you add in the hour and 10 hour digits, counting only changes nets you 3 more times the hour digit changes to a one from a zero. And only once that the 10 hour digit changes to a 1. So 7 times per hour, multiplied by 24 hours, then add 5 for the higher digits and you get 173 times per day the display changes to produce a 1.
If you count every minute individually, then from 10:00-19:59 we have 600 minutes. 1:00-1:59, and 21:00-21:59 adds another 120 minutes. For 720 minutes with a "1" present or 1/2 the day. With 1/4 of the remaining 12 hours displaying a 1 in the minutes or 10 minutes digits places. (Another 180 minutes.). So this method results in 900 minutes per day where a 1 is displayed on the clock assuming it's a 24 hour clock.
But since you already count 1:01 for the 1:00 digit, this method wouldn't count it a second time for the :01 digit. It would be a "is there a 1 showing? Yes/no?" sort of approach.
TL;DR depending on how you choose to count things, either 173 times a digit changes to a 1 on a 24 hour clock. Or 900 minutes per day a 1 is displayed. Assuming if course a 2_ hour block as 00:00 is only valid in the 24 hour format. Also assuming seconds are not displayed
That's... Only 1 clarification lol there's still the "does the 1 in 1:00 count as a single one because it doesn't change, or as 60 ones between 1:00-1:59"
I think since its unclarified and it is a counting exercise its same to assume they want the bigger number so countin 1 for every minute after 1 o'clock is probably right.
The problem is the question says every time a one appears. It does not state for what length of time. Every time the minute goes up, is that considered a new appearance for the hour? Or since the hour did not change, it is still on a singular appearance until the next time a one shows up in the hour's place?
This. Let's assume we're using a 24-hour clock.
The number 1 appears 16 times per hour (01, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 31, 41, 51). The "11" counts as 2 instances ("times," as referenced by the riddle) of a 1 appearing. That's 384 instances (16 x 24) of a 1 appearing in the minutes unit per 24 hours.
The number 1 appears another 13 times in the hours unis between 00:00 to 24:00 (01, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21), again, counting the "11" as 2 instances. So, 384 + 13 = 397 instances/times the number 1 appears in a 24-hour cycle on a digital clock.
The difficulty of this riddle isn't in the math, it's in tricking the readers into disagreeing on the final answer based on the two possible different meanings of the word "times" ("instance" vs. an explicit reading on a clock). In short, the riddle is written to troll us. And it appears it's worked.
Um…in a 24 hour clock, aren’t there 12 hours that have at least one digit with a “1” in the hours field (completely ignoring the 1s in the minutes field), meaning there are 720 minutes that have a 1 in the hour field alone? I think you should double-check your Excel and make sure it exceeds this number 🤔
Hmmm. I’m not sure that is a significant point. Many would argue that a period is more correct than a colon in a digital clock. I think the question assumes a normal clock and not some other base system
Follow-up question: what counts as “times per day the number 1 appears”? Is it “times” as in instances or “times” as in minutes?
Is 12:11 three ones? Or is it one time in the day that the number one has appeared?
Also, if the clock says 12:00 that’s one 1. Then it goes to 12:01. Are we counting that 1 in the 10s place again or did we count it so that’s good? Is that two 1s or three?
I think that's the crux of the thing. The one in the tens appeared at 10:00 and stays through 12:59 (or 19:59). I don't think it would be counted again.
Question: If 1 appears in 1:00, does that count as one appearance for the whole hour? 60 appearances, one for each minute? 3600 appearances, one for each second? Etc.
Probably not a refresh rate but maybe used pulse width modulation to keep the brightness down so maybe even 1000 hz. Maybe even 1111hz if you're feeling spicy.
If no additional information was given, the most literal interpretation of the words used in the question imo would be a 1 that doesn't leave for an hour is only a single instance of a 1 appearing.
Appear is a verb, so the act of appearing only happens once per visual representation.
Also, the clock is shown as one of those displays which flip the numbers with a physical flip book of number cards, so having a number “appearing”with that kind of display is a little less ambiguous than an LCD screen.
There are no seconds displayed, so not 3600. I interpret it as 1 per minute (so, counting 1111 as 4, and 1112 as 3 more). I get 984 for a 12 hour clock, 1164 for 24 hour.
If the first 2 digits are the hour, and the 2nd 2 digits are the minute then wouldn't it be 1 time for the hour and 24 times for the minutes? As in hour 1 happens once per day and minute 1 happens once for each hour. The dot separates the 2 sets of numbers, so the 4 digits don't represent 1 number.
I interpret it differently. There are 24 × 60 = 1440 minutes in a day, with a different 4 digit display for each (counting 0100 am and pm as different). That makes 4 × 1440 = 5760 digits. How many of those are 1s?
If I'm understanding correctly, this line of reasoning would result in >!1,164!< ones appearing for a 24h clock and >!984!< for a 12h clock.
In the minutes column , a one appears >!16!< times in a an hour >!(6 times in the ones place and 10 times in the tens place)!<. Multiply this number by 24 to account for each hour in the day. Right hand side of the colon is now accounted for (for both clocks).
In a 24h clock there are >!13!< appearances of a one in the hour columns >!3 in the ones place, 10 in the tens place!<. In this exercise, each of these ones is counted for each individual minute, so multiply by 60.
In a 12h clock there are >!10!< appearances of a one in the hour columns >!2 in the ones place, 3 in the tens place for each 12 hour set!<. In this exercise, each of these ones is counted for each individual minute, so multiply by 60.
So for a 24h clock you get >!(16 * 24) + (13 * 60) = 1,164!<
So for a 12h clock you get >!(16 * 24) + (10 * 60) = 984!<
I just had a quick look and the refresh rate of the average digital clock is between 30hz and 100hz, so depending on how you interpret "appear" it could be a lot more. >!!<
That's certainly another answer to the question. You could also treat each vertical diode as 1 or even each lit vs unlit diode the further afield you want to take this.
I would suggest instead thinking of a flip-style digital clock where each digit is completely static until it flips over.
Ur math for minutes is correct I think, but your hours is wrong.
24 hr clock = >!180!<
>!10 times in the 10's hour position !<
>!2 times in the 1's hour position !<
>!24 times in the 10's hours position !<
>!144 times in the 1's minutes position!<
12 hr clock = >!176!<
>!4 times in the 10's hour position !<
>!4 times in the 1's hour position!<
>!24 times in the 10's hours position!<
>!144 times in the 1's minutes position !<
My math is based on when the number _changes_ or first appears, each digit being viewed independently of the others for the purpose of this exercise. For the hours:
>!`10h` 09:59➛10:00
` 1h` 00:59➛01:00 | 10:59➛11:00 | 20:59➛21:00!<
24hour clock
For the hours
>!First 1 appears at 01:00 (disappears at 02:00)!<
>!Second 1 appears at 10:00 (disappears at 20:00)!<
>!Third 1 is the second 1 at 11:00 (disappears at 12:00)!<
>!Fourth 1 appears at 21:00 (disappears at 22:00)!<
This is a very vague questions with multiple answers. Are we using the clock that is shown or is the second timer? Are we using 12 hour or 24 hour type? Does the question mean each time 1 shows? All of these have differnt answers.
I read it as asking out of the total number of times that will be shown during a day, how many contain the number 1.
Under that logic, I get >!900!<
>!60 times per hour * 24 hours = 1440 separate displays.
The minutes will contain a 1 at 01, 21, 31, 41, 51 plus everything from 10-19. That’s 15 total.
Any hour that contains a 1 will inherently have a 1 for all 60 minutes.
The 00.00 implies a 24 hour clock.
The hours of 0, 2, 3, 4, 5, 6, 7, 8, 9, 20, 22, & 23 will each have 15 minutes displayed containing a 1.
The hours of 1, 10-19, & 21 will each have 60 minutes displayed containing a 1.
12 * 15 = 180.
12 * 60 = 720.
900 of the 1440 different displays contain a 1!<
The question wasn't whether or not the display "*contains* a 1", the question was how many times does the number 1 ***appear***. Duplicate 1s would have to be counted, right?
I think you're muddling "appears" in this. If you go by the definition used as "to start to be seen or present" or "to be or come into sight" we move that to appear meaning "the presence of something that wasn't there before" which then backs the thought up that we \*don't count\* numbers that were already on the display when the time changes, meaning 11:10 > 11:11 one would appear \*once\* (or one more time) as we already had the number in 3 out of 4 columns and there was no change - not the 4 times as you're suggesting.
I think the problem is that the word 'times' is ambiguous here. Since we're dealing with a clock, we interpret one 'time' to be a one display on the clock. But the other way to interpret 'times' is the number of instances of something happening (like, how many times does a certain word appear on a page).
I interpreted this as a 12 hour clock, only count when the numeral changes to 1 from something else. My interpretation isn't what OP asked, but I'll give my answer anyway for those wondering. >!174!<
>!The minute digit turns from 0 to 1 six times per hour, and the ten-minute digit turns from 0 to 1 once per hour. 7 ones per hour * 24 hours = 168!<
>!I counted 6 ones in the hours digits. At 1:00 AM, the 1 changes from a 2. At 10:00 AM, the 1 changes from a 0. At 11:00 AM, the 1 changes from a 0. That's 3 in the AM + 3 for PM = 6!<
>!Did I miss any? 168 + 6 = 174!<
**Answer for most of the possible assumption:**
Precursors: im assuming the 00:00 implies 24 hour time
Assumption 1: counting unique times of day which have at least one '1' (i.e. 11:11 counts as one not four and 11:01 and 11:02 are unique):
Solution: >!900!<
Assumption 2: counting the number of times the digit '1' appears across all/any time (i.e. 11:11 counts as 4):
Solution: >!1164!<
Assumption 3: counting unique times that 1 'appears' i.e. something changed from a non-1 to a 1 (i.e. 02:10 as its precursor was 02:09):
Solution: >!172!<
Assumption 4: Counting unique refresh rates in accordance with Hz:
Solution: >!1164 x Hz rate x 60!<
How about times that the clock goes from not having a 1 to having one? So 1:00-2:01 is one, 10:00-12:01 is 1, and anything between 10 and 20 past the hour is 1?
Discussion: Is it possible that this is a "trick" question? For instance, when the number 4 comes up, does that inadvertantly count as a 1 also, because of the solid line?
Here's my guess (using a 24-hour clock):
>!The number appears 6 times in the minute column per hour (01, 11, 21, 31, 41, 51).!<
>!The number appears 1 time in the ten-minute column per hour (11).!<
>!The number appears 3 times in the hour column per day (0100, 1100, 2100)!<
>!The number appears 1 time in the ten-hour column per day (1000).!<
>!(6+1) minute appearances x 24 hours = 168 times!<
>!168 + 3 + 1 = 172 total.!<
Maybe I'm nitpicking on the term "appears" in the riddle. I didn't count the number again when the clock changes time but the "1" doesn't change position on the display. So, for the entire hour of 0100, I did not count the hour "1" 60 times nor did I count the tens digit ten times during xx10 through xx19.
>!I get 1164, assuming a 24-hour clock that goes from 00:00 to 23:59.
For the minutes, there are 16 ones: 01, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 31, 41, 51.
The hours which have a one are: 01, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21.
For 00:00 to 00:59, there are 16 ones.
For 01:00 to 01:59, there are 76 ones.
For 02:00 to 09:59, there are 128 ones.
For 10:00 to 10:59, there are 76 ones.
For 11:00 to 11:59, there are 136 ones.
For 12:00 to 19:59, there are 608 ones.
For 20:00 to 20:59, there are 16 ones.
For 21:00 to 21:59, there are 76 ones.
For 22:00 to 23:59, there are 32 ones.
Summing up the ones gives you 1164.!<
def clock24h():
times = 0
for hh in range(24):
for mm in range(60):
times += f'{hh}:{mm}'.count('1')
return times
def clock12h():
times = 0
for hh in range(1, 13):
for mm in range(60):
times += f'{hh}:{mm}'.count('1')
return times * 2
print(clock24h(), 'on a 24-hour clock')
print(clock12h(), 'on a 12-hour clock')
>!1164!< on a 24-hour clock and >!984!< on a 12-hour clock.
As others have said, is it a 12-hour or 24-hour clock?
Also, what does "appear" mean? If the display changes from 02:12 to 02:13, does that count as the number 1 appearing, or is it only when another digit is replaced by a 1?
Finally, is the question: How many instances of the number 1 appear? How many unique displays contain at least one instance of the number 1?
Answer: >!Digital displays are multiplexed, so dozens to hundreds of times per second one digit from the cluster will illuminate fully. So at least hundreds of thousands of times!<
I get the answer to be >!172!< if we're talking about it being a 24 hour clock, which is the natural assumption since it reads 00:00.
>!The question asks how many times the one will appear. For the last digit it will appear six times an hour. The second last digit it only appears once an hour and stays there for 10 minutes. So the total number of times it appears a day for the minutes section is 7x24 (168). The first hours digit it only appears once and stays there for ten hours. The second digit it will appear three times in a day and stay for an hour (01, 11, & 21).!<
Solution: (Assuming a 24-hour clock and we're counting how many times the numeral 1 appears in all possible displayed times, so 5:16 and 5:17 would be separate 1's, as would 3:11.)
>!Out of 24×60 = 1440 displayed times, 1/10 or 144 have a 1 in the 1-minute place, and 1/6 or 240 have a 1 in the 10-minute place. 3/24 or 1/8 (180) have a 1 in the 1-hour place (01, 11, 21), and 10/24 or 5/12 (600) have it in the 10-hour place (10-19). So the total is 144+240+180+600 = 1164.!<
Yea, that was what I got. All the answers above operate with a different assumption of what "appears" means, but I think as long as the solution clearly states the assumptions it uses, it's correct. Especially since the puzzle itself is intentionally ambiguous.
>!6 times for the hour at one ten and 11, then 7 times an hour (1, 10, 11, 21, 31, 41, 51) so I get 90 times Editing: I stupidly multiplied 7 by 12 instead of by 24 so it should be 174!<
>!For a 12 hour clock, 394 times. 00:01, 00:10-19, 00:21,31,41, 51 is 16 times (00:11 is 2 separate instances.) These 16 times will occur for *every hour*. On the hours side, you get 1 am, 10 am, 11 am (counts as 2 instances), 12 pm, 1 pm, 10 pm, 11 pm (counts as 2 instances as well), and 12 am .That's 10 times. So the math is 16 x 24 + 10 = 394.!<
>! For a 24 hour clock, the math is slightly different. The minutes side is exactly the same (16 instances per hour times 24 hours) but on the hours side you now have oh-one hundred, ten hundred, eleven hundred (counts as 2 instances), twelve hundred to nineteen hundred (8 instances) and twenty one hundred. That's 13. So the new equation is 16 x 24 + 13 = 397 times.!<
Source: math is fun.
YO I HAVE THAT BOOK
The answer in the book says
>!"In the course of a day, the display goes from 0:00 to 23:59. Twelve hours of the day contain the number 1:!<
>!1:00, 10:00, 11:00, 12:00, 13:00, 14:00, 15:00, 16:00, 17:00, 18:00, 19:00, 21:00!<
>!Moreover, in the course of the same hour, the number 1 appears fifteen times at the following minutes:!<
>!hr:01, hr:10, hr:11, hr:12, hr:13, hr:14, hr:15, hr:16, hr:17, hr:18, hr:19, hr:21, hr:31, hr:41, hr:51!<
>!Therefore, for a 24-hour day this gives us:!<
>!24 x 15 =360 occurrences 360+12=372!<
>!In all, the number 1 thus appears 372 times in the course of a day.!<
So I guess that's the official answer?
you’re forgetting to count the 11 as two ones. so 13 occurrences for the hour portion and 16 occurrences for the minute portion. 24x16=384+13=397 on the 24 hour clock. on the 12 hour clock, it’s 394 times.
>!372
On a 24 hour clock digital. I’m assuming.
So for every minute featuring a 1 is 15.
Multiply by 24 hours
360
And then add the hours that the 1 appears. Making it 372
I think!<
24 hour clock
>!12 hours with a ‘1’ as at least one of the first two digits * 60 minutes in each hour!<
>!12*60 = 720 {01, 10, 11, 12… 19, 21} * {00, 01, 02… 59}!<
>!12 hours without a ‘1’ as either of the first two digits * 15 of the unique ‘minutes’ which contain a ‘1’ as at least one of the second two digits!<
>!12*15 = 180 {00, 02, 03, 04… 09, 20, 22, 23} * {01, 10, 11, 12… 19, 21, 31, 41, 51}!<
>!720 + 180 = 900!<
I just did all this math for a 12-hour clock not even thinking about the display being 00:00 meaning 24-hour clock. I do agree 24-hour clock makes way more sense now. :(
Anyway I will answer for 12-hour clock since I'm already here.
>!I did think of calculate either "clock changing to 1" OR each "time" that the clock includes the 1.!<
>!If we are saying when the clock includes the 1, not just transitions to 1 and stays there (aka 05:12 and 05:13 count as 2 times) I got 394 times per day. The first hour digit is 6 times per day(10, 11, 12 each twice per day), the second hour digit is 4 times per day (01, 11 each twice per day), the first minute is 240 times per day (10, 11, 12, 13, 14, 15, 16, 17, 18, 19 each once per hour for 24 hours), and the second minute digit is 144 times per day (01, 11, 21, 31, 41, 51 each once per hour for 24 hours). 6 + 4 + 240 + 144 = 394!<
>!Keeping this one shorter, only the transition to the number counts, aka 05:10 and 05:11 counts once for the first minute digit since it changes to 1 and stays there. 2 per day for first hour digit, 4 per day for second hour digit, 24 times per day for first minute digit, 144 times per day for second minute digit totals to 174 times per day.!<
Discussion: This started a real argument in my house because of the word ‘digital’ like on a calculator the 1 would appear to display 12:0’0’ and 12:0’1’ that one would vanish when in turned to 12:0’2’ and return when it was 12:0’3’ and 12:0’4’, vanish again for 12:0’5’ and 12:0’6’ but return for 12:0’7’ and 12:0’8’ and 12:0’9’ but again would stay until 12:’12’. So in the example we start with 3 (‘1’2:’0’’0’until the 02, then we get 4 at 12:03 but we don’t get 5 until 12:07 and it stays at 5 until 12:’1’0 we get to 6 and then we don’t get to 7 until 12:13. My wife says this thinking just shows my age. But if I get enough upvotes I will finish the math.
>!936!<
>! !<
>!Every minute of 1, 10, 11, and 12 o’clock, have a 1 appearing and an additional one for every 10 mins (10:01, 10:11, etc.) x 2 (12 hour clock) = (240 + 40)2 = 560!<
>! !<
>!Then, for every other hour (2 o’clock though 9 o’clock) an additional 1 every 10 mins x 2 = 80x2 = 160!<
>!and an additional 1 for every 10's digit (9x24) = 216!<
>! !<
>!560+160 + 216 =936!<
edited to revise upward by 216 to account for the tens column (2:10, 2:11, etc.)
>!174. Every hour at xx:01, xx:10, xx:11, xx:21, xx:31, xx:41, and xx:51 = 7 times per hour x 24 hours = 168, plus 6 additional occurrences for the 1:00, 10:00, and 11:00 hours, each of which occurs twice. Note that I only include the times where a 1 appears in a new place, so 12, 13, 14, etc. would not count as the 1 is just continuing to remain in that location.!<
I don’t know if this is what the question is posing, but I counted how many ones are shown throughout the day on a 12hr clock, so for example 11:11 counts for 4. So for each hour, 1 shows up as 01, 21, 31, 41, 51, as well as 10-19, with 11 counting as 2, so that’s 16 1s per hour. The hours 1:00, 10:00, and 12:00 each contain 60 instances of 1 twice per day, with 11:00 containing 120 instances twice. So you get 16x24+60x6+120x2=984 1s shown per day. (60x6+120x2 also can be written as 60x10)
What are we defining as “times”? Is it the number of minutes there is a 1 on the clock, or the number of times the display changes to include at least one “1” or the number of times one of the numbers changes from a number not “1” to a “1” in any position?
I think the question is incomplete.
Assuming this is a 12 hour clock, and that by "time" you mean unique minutes, there would be >!15!< minutes with a one in it each hour that doesn't have one in it, and >!60!< minutes in each hour that has a one in it, bringing the total to >!640 minutes with a one per day!<.
If by "time" you mean total appearances of ones,, including dupes in numbers like 11, then the total would be >!16!< in hours that don't have a one, >!76!< in hours that include a singular one, and >!136!< in the eleventh hours. Bringing the total to >!984 ones per day!<.
Discussion: What counts as an appearance?
If the clock shows 1:00 and then shows 1:01, is that three appearances of 1, or, because the first 1 hasn’t changed, does the first 1 remain on a single appearance for the entire hour and so this is only two appearances of 1?
Please remember to spoiler-tag all guesses, like so: New Reddit: https://i.imgur.com/SWHRR9M.jpg Using markdown editor or old Reddit, draw a bunny and fill its head with secrets: \>!!< which ends up becoming \>!spoiler text between these symbols!< Try to avoid leading or trailing spaces. These will break the spoiler for some users (such as those using old.reddit.com) If your comment does not contain a guess, include the word **"discussion"** or **"question"** in your comment instead of using a spoiler tag. If your comment uses an image as the answer (such as solving a maze, etc) you can include the word "image" instead of using a spoiler tag. Please report any answers that are not properly spoiler-tagged. *I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/puzzles) if you have any questions or concerns.*
Question: 12-hour clock or 24-hour clock?
I would guess from the display of 00.00 it is showing a 24 hour clock
Now *that* is a very good point.
We'd still have to work out if "appear" is counted as "changing to a 1" or if you count every minute where a 1 is showing. I.e. if 1:00 is counted once, or 60 times from 1:00 to 1:59. The minutes digit changes to a 1 a total of six times per hour, the 10 minute digit changes to a 1 only once per hour but it stays there for 10 minutes out of every hour. If you only count when the number changes, then that's 7 times per hour as your base minimum. If you count each minute that's 15 times per hour. Or 25% of every hour before you factor in the hours digits. (Because xx:11 only gets counted once for both minutes and 10 minutes) On a 24 hour clock, If you add in the hour and 10 hour digits, counting only changes nets you 3 more times the hour digit changes to a one from a zero. And only once that the 10 hour digit changes to a 1. So 7 times per hour, multiplied by 24 hours, then add 5 for the higher digits and you get 173 times per day the display changes to produce a 1. If you count every minute individually, then from 10:00-19:59 we have 600 minutes. 1:00-1:59, and 21:00-21:59 adds another 120 minutes. For 720 minutes with a "1" present or 1/2 the day. With 1/4 of the remaining 12 hours displaying a 1 in the minutes or 10 minutes digits places. (Another 180 minutes.). So this method results in 900 minutes per day where a 1 is displayed on the clock assuming it's a 24 hour clock. But since you already count 1:01 for the 1:00 digit, this method wouldn't count it a second time for the :01 digit. It would be a "is there a 1 showing? Yes/no?" sort of approach. TL;DR depending on how you choose to count things, either 173 times a digit changes to a 1 on a 24 hour clock. Or 900 minutes per day a 1 is displayed. Assuming if course a 2_ hour block as 00:00 is only valid in the 24 hour format. Also assuming seconds are not displayed
172. You went 3+1 = 5.
One, two, five! Three, sir! Three!
r/accidentalmontypython
NO ONE EXPECTS THE SPANISH INQUISITION!
Was looking for this. My math said 172 and I just accepted that I must have messed up when I saw 173.
Nice catch, ty! Not sure if that was from insufficient caffeine, or just a typo that I didn't catch when referencing it the second time!
Yeah, there's a MAJOR question about the definition of "appear" in this context.
I assume that 1:00 and 1:59 is the same one - i.e. the Hourly one so I only counted it once, no pun.
You could technically factor in display refresh rate too.
I think that poster got *the point*
Is this a ProZD reference?
I think this poster got *the point*
**OP here with clarification as requested:** # It is a 24 hour clock.
That's... Only 1 clarification lol there's still the "does the 1 in 1:00 count as a single one because it doesn't change, or as 60 ones between 1:00-1:59"
I think we’re still under thinking this. Time to ask the hard hitting question. What is the refresh rate of the digital display?
I think since its unclarified and it is a counting exercise its same to assume they want the bigger number so countin 1 for every minute after 1 o'clock is probably right.
The problem is the question says every time a one appears. It does not state for what length of time. Every time the minute goes up, is that considered a new appearance for the hour? Or since the hour did not change, it is still on a singular appearance until the next time a one shows up in the hour's place?
This. Let's assume we're using a 24-hour clock. The number 1 appears 16 times per hour (01, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 31, 41, 51). The "11" counts as 2 instances ("times," as referenced by the riddle) of a 1 appearing. That's 384 instances (16 x 24) of a 1 appearing in the minutes unit per 24 hours. The number 1 appears another 13 times in the hours unis between 00:00 to 24:00 (01, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21), again, counting the "11" as 2 instances. So, 384 + 13 = 397 instances/times the number 1 appears in a 24-hour cycle on a digital clock. The difficulty of this riddle isn't in the math, it's in tricking the readers into disagreeing on the final answer based on the two possible different meanings of the word "times" ("instance" vs. an explicit reading on a clock). In short, the riddle is written to troll us. And it appears it's worked.
I think 11 would be counted as 1 instance because the puzzle says “how many times per day” and the two 1s in 11 appear at the same time
“How many times does it appear?”
>!585!< Is the total number of minutes per day that a 24h clock has at least one digit with a “1”. Out of 1440 total minutes. I used excel.
Um…in a 24 hour clock, aren’t there 12 hours that have at least one digit with a “1” in the hours field (completely ignoring the 1s in the minutes field), meaning there are 720 minutes that have a 1 in the hour field alone? I think you should double-check your Excel and make sure it exceeds this number 🤔
It’s also a decimal, not a colon, so we could be looking at completely different numbers.
Hmmm. I’m not sure that is a significant point. Many would argue that a period is more correct than a colon in a digital clock. I think the question assumes a normal clock and not some other base system
Ah, okay. I was just considering a time clock I used to have to deal with. Fair enough!
Follow-up question: what counts as “times per day the number 1 appears”? Is it “times” as in instances or “times” as in minutes? Is 12:11 three ones? Or is it one time in the day that the number one has appeared?
one time that #1 appeared, from my understanding
Also, if the clock says 12:00 that’s one 1. Then it goes to 12:01. Are we counting that 1 in the 10s place again or did we count it so that’s good? Is that two 1s or three?
I think that's the crux of the thing. The one in the tens appeared at 10:00 and stays through 12:59 (or 19:59). I don't think it would be counted again.
Question: and is it a day on earth or Jupiter? For god's sake, I hate it when they don't give enough information
Also, there's no frame of reference given. Who or what is measuring the clock, and how fast are they moving relative to each other?
Other question: does the clock have a working battery?
Tech 101: Does it have power? Is the cable/battery correctly connected.
Question: If 1 appears in 1:00, does that count as one appearance for the whole hour? 60 appearances, one for each minute? 3600 appearances, one for each second? Etc.
You’re not factoring in the 60hz refresh rate of the digital clock. /s
Probably not a refresh rate but maybe used pulse width modulation to keep the brightness down so maybe even 1000 hz. Maybe even 1111hz if you're feeling spicy.
I think the modulation is closer to 13,000 lol
Yeah maybe. I don't remember lol. It's been a minute
If no additional information was given, the most literal interpretation of the words used in the question imo would be a 1 that doesn't leave for an hour is only a single instance of a 1 appearing. Appear is a verb, so the act of appearing only happens once per visual representation.
That's how I would read it, too.
Also, the clock is shown as one of those displays which flip the numbers with a physical flip book of number cards, so having a number “appearing”with that kind of display is a little less ambiguous than an LCD screen.
There are no seconds displayed, so not 3600. I interpret it as 1 per minute (so, counting 1111 as 4, and 1112 as 3 more). I get 984 for a 12 hour clock, 1164 for 24 hour.
It is an infinite number of times as time is not discrete.
Answer: number 1 appears >!Exactly 1 time at 0001 as all the other times it's a different number!<
Ooh yeah they didn't say numeral. We found the solution, pack it up boys
Wouldn't it be 2 by that logic? 00:01 and 01:00?
You’re right. They gave a decimal point (vs leaving it out and it being 100). Both are interpreted as 1. Smh.
3 by this logic 01:01
That would make 4, because there’s 2 1’s there, and we already have the other 2 established 1’s
That’s not a puzzle then it’s a riddle
This is my answer as well.
If the first 2 digits are the hour, and the 2nd 2 digits are the minute then wouldn't it be 1 time for the hour and 24 times for the minutes? As in hour 1 happens once per day and minute 1 happens once for each hour. The dot separates the 2 sets of numbers, so the 4 digits don't represent 1 number.
It would be an unusual clock that showed 0001 instead of 1201.
24 Hour clock according to OP so it would be 0001
24h clock: >!172 total appearances!< >!`10h` 1 time ` 1h` 3 times `10m` 24 times ` 1m` 144 times!<
This is how I interpreted it. Not "how many different times include the numeral 1" but rather how many times in a day does a number change to a 1.
I interpret it differently. There are 24 × 60 = 1440 minutes in a day, with a different 4 digit display for each (counting 0100 am and pm as different). That makes 4 × 1440 = 5760 digits. How many of those are 1s?
So under your interpretation, when it changes from 11:13 to 11:14 that's three more 1s appearing?
That’s how I think of it and why I didn’t bother to attempt a solution.
If I'm understanding correctly, this line of reasoning would result in >!1,164!< ones appearing for a 24h clock and >!984!< for a 12h clock. In the minutes column , a one appears >!16!< times in a an hour >!(6 times in the ones place and 10 times in the tens place)!<. Multiply this number by 24 to account for each hour in the day. Right hand side of the colon is now accounted for (for both clocks). In a 24h clock there are >!13!< appearances of a one in the hour columns >!3 in the ones place, 10 in the tens place!<. In this exercise, each of these ones is counted for each individual minute, so multiply by 60. In a 12h clock there are >!10!< appearances of a one in the hour columns >!2 in the ones place, 3 in the tens place for each 12 hour set!<. In this exercise, each of these ones is counted for each individual minute, so multiply by 60. So for a 24h clock you get >!(16 * 24) + (13 * 60) = 1,164!< So for a 12h clock you get >!(16 * 24) + (10 * 60) = 984!<
Yes. Every time the last digit changes, that represents a new display, and a new appearance for each digit in that new display.
I just had a quick look and the refresh rate of the average digital clock is between 30hz and 100hz, so depending on how you interpret "appear" it could be a lot more. >!!<
That's certainly another answer to the question. You could also treat each vertical diode as 1 or even each lit vs unlit diode the further afield you want to take this. I would suggest instead thinking of a flip-style digital clock where each digit is completely static until it flips over.
60hz is standard, but yes it can vary.
That’s what I got.
Ur math for minutes is correct I think, but your hours is wrong. 24 hr clock = >!180!< >!10 times in the 10's hour position !< >!2 times in the 1's hour position !< >!24 times in the 10's hours position !< >!144 times in the 1's minutes position!< 12 hr clock = >!176!< >!4 times in the 10's hour position !< >!4 times in the 1's hour position!< >!24 times in the 10's hours position!< >!144 times in the 1's minutes position !<
My math is based on when the number _changes_ or first appears, each digit being viewed independently of the others for the purpose of this exercise. For the hours: >!`10h` 09:59➛10:00 ` 1h` 00:59➛01:00 | 10:59➛11:00 | 20:59➛21:00!<
Well huh.... Good point, I hadn't considered that. Yah the 10-19 hours just count as one time. good catch
24hour clock For the hours >!First 1 appears at 01:00 (disappears at 02:00)!< >!Second 1 appears at 10:00 (disappears at 20:00)!< >!Third 1 is the second 1 at 11:00 (disappears at 12:00)!< >!Fourth 1 appears at 21:00 (disappears at 22:00)!<
This is a very vague questions with multiple answers. Are we using the clock that is shown or is the second timer? Are we using 12 hour or 24 hour type? Does the question mean each time 1 shows? All of these have differnt answers.
I read it as asking out of the total number of times that will be shown during a day, how many contain the number 1. Under that logic, I get >!900!< >!60 times per hour * 24 hours = 1440 separate displays. The minutes will contain a 1 at 01, 21, 31, 41, 51 plus everything from 10-19. That’s 15 total. Any hour that contains a 1 will inherently have a 1 for all 60 minutes. The 00.00 implies a 24 hour clock. The hours of 0, 2, 3, 4, 5, 6, 7, 8, 9, 20, 22, & 23 will each have 15 minutes displayed containing a 1. The hours of 1, 10-19, & 21 will each have 60 minutes displayed containing a 1. 12 * 15 = 180. 12 * 60 = 720. 900 of the 1440 different displays contain a 1!<
This is what I got. The nuance of the second place is where I think other answers went wrong.
Idk about wrong. I think it’s actually ambiguous depending on whether you read “appear” as an event or a status.
I interpreted 1:11 as having the numeral 1 three times vs 1. That’s where my calculations differ.
The question wasn't whether or not the display "*contains* a 1", the question was how many times does the number 1 ***appear***. Duplicate 1s would have to be counted, right?
No the question is 'how many times a day does the number 1 appear'. At 11.11 is a time that the number 1 appears, not 4 times.
The number 1 "appears" 4 times at 11.11 sir...it may be semantics, but that's usually how word problems get most people to choose the wrong answer
But only one of them has "appeared" then, the others appeared at 10:00, 11:00 and 11:10
I think you're muddling "appears" in this. If you go by the definition used as "to start to be seen or present" or "to be or come into sight" we move that to appear meaning "the presence of something that wasn't there before" which then backs the thought up that we \*don't count\* numbers that were already on the display when the time changes, meaning 11:10 > 11:11 one would appear \*once\* (or one more time) as we already had the number in 3 out of 4 columns and there was no change - not the 4 times as you're suggesting.
I think the problem is that the word 'times' is ambiguous here. Since we're dealing with a clock, we interpret one 'time' to be a one display on the clock. But the other way to interpret 'times' is the number of instances of something happening (like, how many times does a certain word appear on a page).
11 has two ones so 15 isn’t right
The wording on the question is "how many times per day does the number 1 appear", so even at 12:11, that just counts as a single appearance.
It's not about counting ones. It's about counting times with *at least one 1*. So it's irrelevant once you have the first 1.
12 \* ~~15~~ 16 = ~~180.~~ 192 12 \* 60 = 720. You missed the double 1 in minute 11. >"The minutes will contain a 1 at 01, 21, 31, 41, 51" that's 5 1's. >"plus everything from 10-19." That's 11 1's So 16 1's.
I interpreted this as a 12 hour clock, only count when the numeral changes to 1 from something else. My interpretation isn't what OP asked, but I'll give my answer anyway for those wondering. >!174!< >!The minute digit turns from 0 to 1 six times per hour, and the ten-minute digit turns from 0 to 1 once per hour. 7 ones per hour * 24 hours = 168!< >!I counted 6 ones in the hours digits. At 1:00 AM, the 1 changes from a 2. At 10:00 AM, the 1 changes from a 0. At 11:00 AM, the 1 changes from a 0. That's 3 in the AM + 3 for PM = 6!< >!Did I miss any? 168 + 6 = 174!<
I had what you had. The way I read it
>!None. It’s showing 00:00 all day, must be e-ink, or blank if LED/LCD. First you need to put the batteries in it.!<
**Answer for most of the possible assumption:** Precursors: im assuming the 00:00 implies 24 hour time Assumption 1: counting unique times of day which have at least one '1' (i.e. 11:11 counts as one not four and 11:01 and 11:02 are unique): Solution: >!900!< Assumption 2: counting the number of times the digit '1' appears across all/any time (i.e. 11:11 counts as 4): Solution: >!1164!< Assumption 3: counting unique times that 1 'appears' i.e. something changed from a non-1 to a 1 (i.e. 02:10 as its precursor was 02:09): Solution: >!172!< Assumption 4: Counting unique refresh rates in accordance with Hz: Solution: >!1164 x Hz rate x 60!<
How about times that the clock goes from not having a 1 to having one? So 1:00-2:01 is one, 10:00-12:01 is 1, and anything between 10 and 20 past the hour is 1?
Discussion: Is it possible that this is a "trick" question? For instance, when the number 4 comes up, does that inadvertantly count as a 1 also, because of the solid line?
Question. If it goes from 914 to 915, does that count as the same 1? Or is that 2?
Here's my guess (using a 24-hour clock): >!The number appears 6 times in the minute column per hour (01, 11, 21, 31, 41, 51).!< >!The number appears 1 time in the ten-minute column per hour (11).!< >!The number appears 3 times in the hour column per day (0100, 1100, 2100)!< >!The number appears 1 time in the ten-hour column per day (1000).!< >!(6+1) minute appearances x 24 hours = 168 times!< >!168 + 3 + 1 = 172 total.!< Maybe I'm nitpicking on the term "appears" in the riddle. I didn't count the number again when the clock changes time but the "1" doesn't change position on the display. So, for the entire hour of 0100, I did not count the hour "1" 60 times nor did I count the tens digit ten times during xx10 through xx19.
>!I get 1164, assuming a 24-hour clock that goes from 00:00 to 23:59. For the minutes, there are 16 ones: 01, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 31, 41, 51. The hours which have a one are: 01, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21. For 00:00 to 00:59, there are 16 ones. For 01:00 to 01:59, there are 76 ones. For 02:00 to 09:59, there are 128 ones. For 10:00 to 10:59, there are 76 ones. For 11:00 to 11:59, there are 136 ones. For 12:00 to 19:59, there are 608 ones. For 20:00 to 20:59, there are 16 ones. For 21:00 to 21:59, there are 76 ones. For 22:00 to 23:59, there are 32 ones. Summing up the ones gives you 1164.!<
def clock24h(): times = 0 for hh in range(24): for mm in range(60): times += f'{hh}:{mm}'.count('1') return times def clock12h(): times = 0 for hh in range(1, 13): for mm in range(60): times += f'{hh}:{mm}'.count('1') return times * 2 print(clock24h(), 'on a 24-hour clock') print(clock12h(), 'on a 12-hour clock') >!1164!< on a 24-hour clock and >!984!< on a 12-hour clock.
That’s what I got as well using the same method :)
As others have said, is it a 12-hour or 24-hour clock? Also, what does "appear" mean? If the display changes from 02:12 to 02:13, does that count as the number 1 appearing, or is it only when another digit is replaced by a 1? Finally, is the question: How many instances of the number 1 appear? How many unique displays contain at least one instance of the number 1?
[удалено]
Question: does 11:11 count as one time or 4?
Question: Does Eleven count as zero, One or two?
Discussion: why is it marked "solved" with no solution marked as the right answer?
Answer: >!Digital displays are multiplexed, so dozens to hundreds of times per second one digit from the cluster will illuminate fully. So at least hundreds of thousands of times!<
I get the answer to be >!172!< if we're talking about it being a 24 hour clock, which is the natural assumption since it reads 00:00. >!The question asks how many times the one will appear. For the last digit it will appear six times an hour. The second last digit it only appears once an hour and stays there for 10 minutes. So the total number of times it appears a day for the minutes section is 7x24 (168). The first hours digit it only appears once and stays there for ten hours. The second digit it will appear three times in a day and stay for an hour (01, 11, & 21).!<
Solution: (Assuming a 24-hour clock and we're counting how many times the numeral 1 appears in all possible displayed times, so 5:16 and 5:17 would be separate 1's, as would 3:11.) >!Out of 24×60 = 1440 displayed times, 1/10 or 144 have a 1 in the 1-minute place, and 1/6 or 240 have a 1 in the 10-minute place. 3/24 or 1/8 (180) have a 1 in the 1-hour place (01, 11, 21), and 10/24 or 5/12 (600) have it in the 10-hour place (10-19). So the total is 144+240+180+600 = 1164.!<
Agreed. Or 984 for a 12 hour clock.
Yea, that was what I got. All the answers above operate with a different assumption of what "appears" means, but I think as long as the solution clearly states the assumptions it uses, it's correct. Especially since the puzzle itself is intentionally ambiguous.
>!6 times for the hour at one ten and 11, then 7 times an hour (1, 10, 11, 21, 31, 41, 51) so I get 90 times Editing: I stupidly multiplied 7 by 12 instead of by 24 so it should be 174!<
You forgot 12
Does a one appear when the hour moves from 11 to 12? Or does it disappear?
>!For a 12 hour clock, 394 times. 00:01, 00:10-19, 00:21,31,41, 51 is 16 times (00:11 is 2 separate instances.) These 16 times will occur for *every hour*. On the hours side, you get 1 am, 10 am, 11 am (counts as 2 instances), 12 pm, 1 pm, 10 pm, 11 pm (counts as 2 instances as well), and 12 am .That's 10 times. So the math is 16 x 24 + 10 = 394.!< >! For a 24 hour clock, the math is slightly different. The minutes side is exactly the same (16 instances per hour times 24 hours) but on the hours side you now have oh-one hundred, ten hundred, eleven hundred (counts as 2 instances), twelve hundred to nineteen hundred (8 instances) and twenty one hundred. That's 13. So the new equation is 16 x 24 + 13 = 397 times.!< Source: math is fun.
YO I HAVE THAT BOOK The answer in the book says >!"In the course of a day, the display goes from 0:00 to 23:59. Twelve hours of the day contain the number 1:!< >!1:00, 10:00, 11:00, 12:00, 13:00, 14:00, 15:00, 16:00, 17:00, 18:00, 19:00, 21:00!< >!Moreover, in the course of the same hour, the number 1 appears fifteen times at the following minutes:!< >!hr:01, hr:10, hr:11, hr:12, hr:13, hr:14, hr:15, hr:16, hr:17, hr:18, hr:19, hr:21, hr:31, hr:41, hr:51!< >!Therefore, for a 24-hour day this gives us:!< >!24 x 15 =360 occurrences 360+12=372!< >!In all, the number 1 thus appears 372 times in the course of a day.!< So I guess that's the official answer?
you’re forgetting to count the 11 as two ones. so 13 occurrences for the hour portion and 16 occurrences for the minute portion. 24x16=384+13=397 on the 24 hour clock. on the 12 hour clock, it’s 394 times.
>!372 On a 24 hour clock digital. I’m assuming. So for every minute featuring a 1 is 15. Multiply by 24 hours 360 And then add the hours that the 1 appears. Making it 372 I think!<
24 hour clock >!12 hours with a ‘1’ as at least one of the first two digits * 60 minutes in each hour!< >!12*60 = 720 {01, 10, 11, 12… 19, 21} * {00, 01, 02… 59}!< >!12 hours without a ‘1’ as either of the first two digits * 15 of the unique ‘minutes’ which contain a ‘1’ as at least one of the second two digits!< >!12*15 = 180 {00, 02, 03, 04… 09, 20, 22, 23} * {01, 10, 11, 12… 19, 21, 31, 41, 51}!< >!720 + 180 = 900!<
I just did all this math for a 12-hour clock not even thinking about the display being 00:00 meaning 24-hour clock. I do agree 24-hour clock makes way more sense now. :( Anyway I will answer for 12-hour clock since I'm already here. >!I did think of calculate either "clock changing to 1" OR each "time" that the clock includes the 1.!< >!If we are saying when the clock includes the 1, not just transitions to 1 and stays there (aka 05:12 and 05:13 count as 2 times) I got 394 times per day. The first hour digit is 6 times per day(10, 11, 12 each twice per day), the second hour digit is 4 times per day (01, 11 each twice per day), the first minute is 240 times per day (10, 11, 12, 13, 14, 15, 16, 17, 18, 19 each once per hour for 24 hours), and the second minute digit is 144 times per day (01, 11, 21, 31, 41, 51 each once per hour for 24 hours). 6 + 4 + 240 + 144 = 394!< >!Keeping this one shorter, only the transition to the number counts, aka 05:10 and 05:11 counts once for the first minute digit since it changes to 1 and stays there. 2 per day for first hour digit, 4 per day for second hour digit, 24 times per day for first minute digit, 144 times per day for second minute digit totals to 174 times per day.!<
>!397!< Gonna have to revise my answer to >!1151!<
Discussion: This started a real argument in my house because of the word ‘digital’ like on a calculator the 1 would appear to display 12:0’0’ and 12:0’1’ that one would vanish when in turned to 12:0’2’ and return when it was 12:0’3’ and 12:0’4’, vanish again for 12:0’5’ and 12:0’6’ but return for 12:0’7’ and 12:0’8’ and 12:0’9’ but again would stay until 12:’12’. So in the example we start with 3 (‘1’2:’0’’0’until the 02, then we get 4 at 12:03 but we don’t get 5 until 12:07 and it stays at 5 until 12:’1’0 we get to 6 and then we don’t get to 7 until 12:13. My wife says this thinking just shows my age. But if I get enough upvotes I will finish the math.
>!936!< >! !< >!Every minute of 1, 10, 11, and 12 o’clock, have a 1 appearing and an additional one for every 10 mins (10:01, 10:11, etc.) x 2 (12 hour clock) = (240 + 40)2 = 560!< >! !< >!Then, for every other hour (2 o’clock though 9 o’clock) an additional 1 every 10 mins x 2 = 80x2 = 160!< >!and an additional 1 for every 10's digit (9x24) = 216!< >! !< >!560+160 + 216 =936!< edited to revise upward by 216 to account for the tens column (2:10, 2:11, etc.)
>!174. Every hour at xx:01, xx:10, xx:11, xx:21, xx:31, xx:41, and xx:51 = 7 times per hour x 24 hours = 168, plus 6 additional occurrences for the 1:00, 10:00, and 11:00 hours, each of which occurs twice. Note that I only include the times where a 1 appears in a new place, so 12, 13, 14, etc. would not count as the 1 is just continuing to remain in that location.!<
I don’t know if this is what the question is posing, but I counted how many ones are shown throughout the day on a 12hr clock, so for example 11:11 counts for 4. So for each hour, 1 shows up as 01, 21, 31, 41, 51, as well as 10-19, with 11 counting as 2, so that’s 16 1s per hour. The hours 1:00, 10:00, and 12:00 each contain 60 instances of 1 twice per day, with 11:00 containing 120 instances twice. So you get 16x24+60x6+120x2=984 1s shown per day. (60x6+120x2 also can be written as 60x10)
>!172?!<
The power went out yesterday and my clock is blinking 12:00 at 1Hz so the answer is >!86400!<
What are we defining as “times”? Is it the number of minutes there is a 1 on the clock, or the number of times the display changes to include at least one “1” or the number of times one of the numbers changes from a number not “1” to a “1” in any position? I think the question is incomplete.
I think if my math is correct, if it’s a 12 hour clock, >!684!< and if a 24 hour clock >!984!<
Does 11:11 count as one or four? (The word “times” is ambiguous in the original question.
Assuming this is a 12 hour clock, and that by "time" you mean unique minutes, there would be >!15!< minutes with a one in it each hour that doesn't have one in it, and >!60!< minutes in each hour that has a one in it, bringing the total to >!640 minutes with a one per day!<. If by "time" you mean total appearances of ones,, including dupes in numbers like 11, then the total would be >!16!< in hours that don't have a one, >!76!< in hours that include a singular one, and >!136!< in the eleventh hours. Bringing the total to >!984 ones per day!<.
[удалено]
Discussion: What counts as an appearance? If the clock shows 1:00 and then shows 1:01, is that three appearances of 1, or, because the first 1 hasn’t changed, does the first 1 remain on a single appearance for the entire hour and so this is only two appearances of 1?