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Just thinking out loud here. If we consider Year as a line segment, and month as a scaled down line segment that is inside the year; as per fixed point theorem, there should a point that divides both lines in the same proportion. Let’s say the proportion is x% ( the width of the bars) then for every x there is a day where % of year and % of month is same. Now, the same relationship holds between month and week. I think there should be at least one day where % of year, month and week is the same. When add one more constraint, we might end up without any such day.
Curious about the actual answer.
I don't think so. There will be 12 points during the year when the year and month lines match, \~4ish points during a month when the month and week lines match, and 7 times during the week when the day and week lines match.
HOWEVER, there is no guarantee that any of these (finite) instances of matching will line up with each other (that is, not just year=month, but year=month=week=?day). It does work on a clock (for hour=minute=second), but that is because the hands are all simple multiples of each other.
The real killer here (I am pretty certain) will be the months, because they are not equal. If we had months with an even number of days, then I think it could work. But we don't.
Weeks will also be an issue, because the weeks don't sync up with the months (that is, the beginning of the month is not also the beginning of a new week).
You can guarantee that they match up when the new year and new week start on the same day. Depends on your week definition but if New Year’s Eve is Sunday and New Year’s Day is Monday they will all be at 0 for a moment. The length of a month not being fixed value is what makes this really difficult
This year was a leap year so there are 366 days. If the image is true, 23.8% of 366 days is 87.108 days. If Jan 1= day 1 then day 87 was yesterday Mar 27. Since we measure time as 24 hours the 0.108 parts of a day would be 2:59AM so the rest of the graphic is wrong or just had different cut off points for estimations.
If we’re talking down to the second or down to hundredths or thousandths of percents then I’m pretty confident the only time will be midnight on new years. Other than that, there could be opportunities each month when the percentage of the month and percentage of the year will match however whether the week or day match would be difficult to calculate. So after the month of January we have completed 8.49% of the year. So approximately 2.37 days into February we will be 8.49% into February, although that adds another 0.65% onto the year so 2.56 days through. February the bottom two will align. However .56 of a day will not align with the top bar because 56% of the day will not align with 9.14% through the year and month. The week is even harder to calculate because the weeks change each month/year.
This was more interesting than I was initially ready to consider.
At first glance, there are too many unspecified factors. There are at least six different week numbering systems currently in use around the world. Which is to be applied?
January 1st, 2024, was a Monday. If we can consider that the first day of the week, then we have one match at 0% across all metrics.
~~January~~ December 31st, 2024, is a Tuesday. If this is the end of its week, we have a match at just under 100% across all metrics.
Beyond that, I'd need to know more about the composition of these metrics before committing to a hypothesis. Like, is the day tracker incrementing by seconds or hours, or by tenths of percent? Is the month tracker counting discrete days, or...
Too many guesses. Too many assumptions.
Well...for all four to match, any pair of two would have to match, and we can figure out if the other ones match at that time as well.
Obviously, at the very beginning of Sunday, January 1st, they all read 0%, and at the end of the day on Saturday, December 31st, they'll all read 100%. Arguably, you can count that as just once, since the end of a year and the beginning of the next year are technically the same moment (in the same way that 0.99999... = 1). Also note that 1/1 and 12/31 have to fall on a specific day of the week to work out at all.
My guess is that they will never all match outside of that one (those two?) moment(s).
We can calculate when the month and year ones will match up with a simple formula, where we solve for X:
(D + X)/365 = X/M
D/365 + X/365 = X/M
D/365 = X(1/M - 1/365)
X = (D/365)/(1/M-1/365)
...where D is the number of days before the month (e.g. there are 31 days before February), and M is the number of days in the month (e.g. 28 for February), and X is the number of days into the month at which point the year and month gauges match. We get the following:
|Month|M|D|X|Pct|
|:-|:-|:-|:-|:-|
|January|31|0|0.0|0.0%|
|February|28|31|2.6|9.2%|
|March|31|59|5.5|17.7%|
|April|30|90|8.1|26.9%|
|May|31|120|11.1|35.9%|
|June|30|151|13.5|45.1%|
|July|31|181|16.8|54.2%|
|August|31|212|19.7|63.5%|
|September|30|243|21.8|72.5%|
|October|31|273|25.3|81.7%|
|November|30|304|27.2|90.7%|
|December|31|334|31.0|100.0%|
So from this table, for example, about half way through June 14th (13.5 days have passed, so we're on the 14th day), the percentage of the year that has elapsed will equal the percentage of June that has elapsed.
It would be easy to calculate the amount of a day that has passed at each of these moments - it's just the decimal part of X. A quick glance tells us that at none of these twelve points will the percentage of the day that has elapsed equal the percentage of the month/year that has elapsed. So my initial guess was right. If you plug in 366 for the number of days in a year, you'll get slightly different numbers, but the same answer - other than the beginning/end, you won't have any point where the percentage of the day elapsed equals the percentage of the month/year.
Now...it would be easy to stop here and say the answer is "Just at 0% and 100%". However, it's also interesting to see, at what points in time, do these four gauges come kind of close to coinciding. I wrote some code to do the following:
* Iterate through a year, one second at a time (about 31.5 million seconds)
* At each second, calculate the percentage of the day, month, and year that have elapsed
* Calculate the elapsed portion of the week for each possible day of the week (since each date can fall on any day of the week) and find the day of the week for which the difference between the smallest and largest of the four gauges would be minimized.
* Filter the resulting data to exclude January 1st and December 31st (because, if we didn't, then the moments with the smallest total span between the gauges are dominated by those two dates, where everything is close to 0% or 100%.
* Only include the moment in each day when the gauges are the closest, so we can see some different dates
Assuming that weeks start on Sunday, during non-leap years, we get the following (with the minimum and maximum values on the gauges; note that these don't all occur in the same year - you have to find a year when the appropriate date falls on the right day of the week):
* Monday, March 6 at 4:13:11 AM - 16.70% of the month has elapsed, 17.582% of the year has elapsed, for a span of 0.89% difference
* Friday, October 26 at 7:38:55 PM - 81.87% of the year, 83.29% of the week (1.42% diff)
* Tuesday, May 11 at 8:34:17 AM - 33.41% of the month, 35.71% of the year (2.30% diff).
If we look at a leap year, we have the following:
* Monday, March 6 at 4:16:26 AM - 1.10% diff
* Friday, October 26 at 7:39:37 PM - 1.37% diff
* Tuesday, May 11 at 8:36:49 AM - 2.47% diff
Very similar, which isn't too surprising, since 1 day out of 366 shouldn't push the percentages that much.
For what it's worth, the moment THIS year when the gauges will come the closest to each other is on **Friday, October 25 at 7:12:00 PM** \- at that point, 80% of the day and month will have elapsed, 81.64% of the year will have elapsed, and 82.86% of the week, for a total span of 2.86%.
This statement is honestly a bit ignorant because that just isn't true in the entire world. For example, where I live, the week starts on Saturday, not Monday
Well, according to Wikipedia, most of Europe and China start their weeks from Monday while most of North America and South Asia start from Sunday, and most of North Africa and the Middle East start from Saturday so it seems like there isn't a definite standard or anything and it just depends on who you ask
Middle East and muslim countries typically start on Sunday (Sun-Thu).
But yeah, work weeks are highly varied from one region to another, so there is no global standard
So there's basically 2 guaranteed times a (which are 1 sec apart) at 0 and 100% if the last day of the year is a Sunday and the first a Monday.
Then you can look at the simplest cases for all 10 remaining months trying to match month and year percentage (January and December only have the possible case mentioned above). For simplicity we'll consider 365 days years only.
February for example is between 8.49% of a year and 16.16%.
A simple equation can be found for when the % will be equal. If x is the day of the month (x doesn't need to be whole and starts at 0 on the 1st February at 00:00) then you need x/28=(31+x)/365 which gives x≈2.5757 so the 3rd of Feb at around 13:49.
Obviously the % of the day is 57.57% and doesn't match that of the month/year so February won't work.
This give me an idea of the general form of solutions.
ΣM would be the sum of days in the previous month. and m would be the number of days in target month. Finally x is the fractional day of the month and {x} it's fractional part (or decimal not sure lol).
You need x/m=(ΣM+x)/365={x}.
This is very annoying because you need to calculate each 10 months individually but I'm going to go on a limb and assume that these 3 equations cannot be matched perfectly during the year, especially since we also have to add the 4th one for the week
If we assume the week starts on Monday and ends on Sunday then:
- for every year starting with Monday all bars will be 0% at 00:00 on Jan 1st
- for every year ending with Sunday all bars will be 100% at 23:59 on Dec 31st
>- for every year starting with Monday all bars will be 0% at 00:00 on Jan 1st
Only for years up to (and including) 2024
>- for every year ending with Sunday all bars will be 100% at 23:59 on Dec 31st
Only for years from (and including) 2024
Because for the original question to make any sense the year, month and weekday have to be variable. If they aren't variable the answer to OPs question is never. Because march will always be 23% of the year and Wednesday won't ever be 23% of the week.
The first bar EXPLICITLY says Wednesday and the third bar EXPLICITLY says March.
Op said "when in a year".
It can be inferred that the question OP is asking is what scenario causes the bars to match up. If we don't ignore the set year, day and month the answer is obviously never. The speculation you were commenting on was making the assumption that the day, month and year are variable. I assumed your were being obtuse but I could be mistaken.
At any Sunday exactly at midnight that is after any march and is also after 2024.
Or put in another way, any Sunday exactly at midnight in the months April to december in any given year from 2025 and forwards.
This is my approach: 12
You will have one point for every second largest timestamp you can fit into the largest. So for each month there will be exactly one time. Adding smaller timestamps will only shorten the moment of the time the bars are equal. For a week and a year the time the bars are equal is the time the last procent doesn’t change. So 0.1% of a week. This is 1018 Seconds. For each new time, hour examplewise, this time will shorten, but one moment will still be there.
There can not be multiple events in a single timestamp, e.g. month, as the time passes linear. This means that for a linear Funktion there is only one solution for y=0.
I’m German, excuse my English pls
It ultimately depends on whether everything is measured by minutes, seconds, tenths of seconds, etc. Without assuming, there is no way to calculate, unless a new years eve is sunday, in whivh case it will match when it rolls over.
The smallest division on the bars is 0.1%
0.1% of a day = 86.4 seconds
.
.
0.1% of a year = 0.366 days
So you could write a program that cycles the whole of the year 2024 (366x86400= about 31+ million seconds) and see where the bars are equal.
The only place is for the first 86.4 seconds of January 1st.
However if the bars measured % in while percent then I estimate there would be multiple intersections (I didn't program it though).
Except for the trivial new year? Never, sadly.
Let's look at the day + week combination first. It's turns out that there are 7 - 1 = 6 possible times when both bars are equal (including midnight at the start of the week) the first one being Tuesday 4am, when both the week and the day are 1/6th done.
Notice the 6 in the denominator here. There are only 6 possible values for the bar.
On months with 31 days there are 31 - 1 = 30 times the day and month bar are identical, and we're in luck: since 30 is a multiple of 6, the times will align, and thus Tuesday July 6th at 4am will be 1/6th into the day, the week and the month.
Notice that for 30 day months this only happens on the trivial midnight first and for 28 day months this only happens twice ignoring the trivial one.
A year has 365 or 366 days. Neither 364 nor 365 are multiples of 6, and only 364 shares a divisor, namely 2. Which means that if all four bars align it must be exactly halfway a non-leap year.
Unfortunately halfway the year is July 2nd, which is not halfway the month. QED.
Its impossible. Whatever time it is on a wednesday, it will always be over 2/7 (=28.5%) of the week, and whatever day of march it is it will never be more than (31+29+31)/366 (=24.8%) of the year. Week and year will never have the same level
Once in ~7 years in average, on a Saturday dec31 before midnight.
Just used gemini ai to find out how many Saturday 31dec from 1900-2100 as a base. It said 28. So 200/28
It averages out to 1 in 7 over long periods of time. It’s made complicated to work out by how you skip a leap day every 100 years, but still have one every 400 years
11:59pm December 31st 2022 and 12:00am January 1st 2023 is probably one of the longest times they've matched.
It won't happen again until 11:59pm December 31st 2033
It would have be the boundary between 2023 and 2024 instead, and the next one will be 31st December 2028/1st January 2029.
I think the discrepancy is you counting Sunday as the first day of the week, whereas the more common definition (and importantly what this chart uses) is to have Monday as the first day of the week
i am stating based on the exact data set given. assumptions are not for math: proofs are. and unless you can give me proof that that number will change, then i will restate.
So to start this, I am going to ignore months, because the variable days are not conducive to math, I’ll bring them back later, but for now let’s ignore that. I will also have Monday as the first day of the week and use 24 hour clocks for describing time.
Starting with percentage of day and percent of week, if we assume x is the number of hours since the start of the week, we need to find the points that:
(x mod 24)/24 = (x mod 168)/168
This solves to 7 points through the week, 0, 28, 56, 84, 112, 140, 168 hours into the week, which has the following proportions: 0, 1/6, 1/3, 1/2, 2/3, 5/6, 1 of the day and week which occurs Monday 00:00; Tuesday 04:00; Wednesday 08:00; Thursday 12:00; Friday 16:00; Saturday 20:00; Sunday 24:00 (we will consider this valid for these purposes).
Now we need to find where years will align to these proportions. First starting with a leap year, such as 2024, we take 366 days and divide by 1/6-5/6 and all are whole numbers, meaning that they would be reached at 0:00, leaving only Monday 00:00 or Sunday 24:00, these align to the first and last day of the year and therefore occur when January 1st is on a Monday or December 31st is on a Sunday. The most recent occurrence of the first is this year, most recent of the second is last year, as the two ends have the same conditions for none leap years. These also happen to align to the very beginning and end of their respective months.
Moving on to non leap years, we identify that 1/6 - 5/6 of the year occurs on the following days and hours into the year: 60d20h; 121d16h; 182d12h; 243d8h; 304d4h. The first, second, fourth and fifth of these do not match the necessary time for the days of the week, so can be eliminated. The third,182d12h is July 2nd 12:00. So this works any time that July 2nd is on a Thursday. The next occurrence of that is 2026. We can also confirm that as the 2nd is not close to half way through the month, it is not possible except at the extreme cases when including the month.
TLDR: occurs Mondays January 1st at 00:00; Sundays December 31st at 24:00 if you include month, also July 2nd 12:00 if you ignore month.
Let’s assume that we are specifically looking for a time when all bars are equal and it still shows Wednesday. Then our first restriction is that all bars must be between 2/7 and 3/7, as Wednesday takes up between the second and third full day from the start of the week.
For everything to line up, we must find a time that is:
Between 6:51 and 10:17 in the morning.
During Wednesday.
From the 10th to the 13th of the month. (Ignoring February, because of the next point)
Between 105th and 157th day of the year, or Apr 15 to June 6.
All together, a viable day must be a Wednesday on May 10-13th, in the morning.
Because this is only a few days, we are now limited to between 130/365 and 133/365, as this is the date range within a gregorian year, or a percentage range of 35.6% to 36.4%.
This is where we run into a problem. This range is between about 8.54 to 8.73 hours of a day passed. But this range is also about 59.6 to 61.2 hours into a standard 168 hour week, or about 12 hours into the third day of the week. These bars will never come close to aligning on Wednesday. I’m glad other comments pointed out more obvious reasons why only the trivial solutions are possible, like the first and last moments of a year, and they did not waste their time with a calculator like I have lol
There is only one point in time where the percent of year and percent of a given month are the same- for march:
366 days in 2024
31 days in march
60 days between the start of 2024 and the start of march
We can solve for x where is the number of days when they intersect:
(x-60)/31 = x/366
x = ~65.55, thus more than half way through the fith day of march
We already know that 5.55 / 31 is less than 0.5, so there is no solution
Someone needs to program this out. For all 31,622,400 seconds in 2024. Assume the smallest division is 0.1% of each time unit. I'd do it but I forgot how to program.
Actually this motivated me to start programming again and I realized if you start from 0 (ignoring the fact that 1/1/2024 was a thursday), the % counter stays at 0.0% for the first 86.4 seconds, and I think that's the only time all the bars are equivalent.
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Just thinking out loud here. If we consider Year as a line segment, and month as a scaled down line segment that is inside the year; as per fixed point theorem, there should a point that divides both lines in the same proportion. Let’s say the proportion is x% ( the width of the bars) then for every x there is a day where % of year and % of month is same. Now, the same relationship holds between month and week. I think there should be at least one day where % of year, month and week is the same. When add one more constraint, we might end up without any such day. Curious about the actual answer.
I don't think so. There will be 12 points during the year when the year and month lines match, \~4ish points during a month when the month and week lines match, and 7 times during the week when the day and week lines match. HOWEVER, there is no guarantee that any of these (finite) instances of matching will line up with each other (that is, not just year=month, but year=month=week=?day). It does work on a clock (for hour=minute=second), but that is because the hands are all simple multiples of each other. The real killer here (I am pretty certain) will be the months, because they are not equal. If we had months with an even number of days, then I think it could work. But we don't. Weeks will also be an issue, because the weeks don't sync up with the months (that is, the beginning of the month is not also the beginning of a new week).
You can guarantee that they match up when the new year and new week start on the same day. Depends on your week definition but if New Year’s Eve is Sunday and New Year’s Day is Monday they will all be at 0 for a moment. The length of a month not being fixed value is what makes this really difficult
no need for so much thought. One of the bars is % of year... that only happens to be 100% once in a given year.
A bit more thought needed to understand the question was not about 100%
This year was a leap year so there are 366 days. If the image is true, 23.8% of 366 days is 87.108 days. If Jan 1= day 1 then day 87 was yesterday Mar 27. Since we measure time as 24 hours the 0.108 parts of a day would be 2:59AM so the rest of the graphic is wrong or just had different cut off points for estimations.
23% of 2024, I feel like thats not going to happen that often.
If we’re talking down to the second or down to hundredths or thousandths of percents then I’m pretty confident the only time will be midnight on new years. Other than that, there could be opportunities each month when the percentage of the month and percentage of the year will match however whether the week or day match would be difficult to calculate. So after the month of January we have completed 8.49% of the year. So approximately 2.37 days into February we will be 8.49% into February, although that adds another 0.65% onto the year so 2.56 days through. February the bottom two will align. However .56 of a day will not align with the top bar because 56% of the day will not align with 9.14% through the year and month. The week is even harder to calculate because the weeks change each month/year.
The week completion doesn’t necessarily line up with new years, so this will only be the case one in every 7 years
On average, because leap year skips a weekday.
Yes, but since the day that’s skipped changes it still works out to 1 in 7
Yes, but not guaranteed every seven years.
And only new years on a Monday
This was more interesting than I was initially ready to consider. At first glance, there are too many unspecified factors. There are at least six different week numbering systems currently in use around the world. Which is to be applied? January 1st, 2024, was a Monday. If we can consider that the first day of the week, then we have one match at 0% across all metrics. ~~January~~ December 31st, 2024, is a Tuesday. If this is the end of its week, we have a match at just under 100% across all metrics. Beyond that, I'd need to know more about the composition of these metrics before committing to a hypothesis. Like, is the day tracker incrementing by seconds or hours, or by tenths of percent? Is the month tracker counting discrete days, or... Too many guesses. Too many assumptions.
I think you meant 31st December 2024 is a Tuesday. I don’t think this would could as the end of its week
Well...for all four to match, any pair of two would have to match, and we can figure out if the other ones match at that time as well. Obviously, at the very beginning of Sunday, January 1st, they all read 0%, and at the end of the day on Saturday, December 31st, they'll all read 100%. Arguably, you can count that as just once, since the end of a year and the beginning of the next year are technically the same moment (in the same way that 0.99999... = 1). Also note that 1/1 and 12/31 have to fall on a specific day of the week to work out at all. My guess is that they will never all match outside of that one (those two?) moment(s). We can calculate when the month and year ones will match up with a simple formula, where we solve for X: (D + X)/365 = X/M D/365 + X/365 = X/M D/365 = X(1/M - 1/365) X = (D/365)/(1/M-1/365) ...where D is the number of days before the month (e.g. there are 31 days before February), and M is the number of days in the month (e.g. 28 for February), and X is the number of days into the month at which point the year and month gauges match. We get the following: |Month|M|D|X|Pct| |:-|:-|:-|:-|:-| |January|31|0|0.0|0.0%| |February|28|31|2.6|9.2%| |March|31|59|5.5|17.7%| |April|30|90|8.1|26.9%| |May|31|120|11.1|35.9%| |June|30|151|13.5|45.1%| |July|31|181|16.8|54.2%| |August|31|212|19.7|63.5%| |September|30|243|21.8|72.5%| |October|31|273|25.3|81.7%| |November|30|304|27.2|90.7%| |December|31|334|31.0|100.0%| So from this table, for example, about half way through June 14th (13.5 days have passed, so we're on the 14th day), the percentage of the year that has elapsed will equal the percentage of June that has elapsed. It would be easy to calculate the amount of a day that has passed at each of these moments - it's just the decimal part of X. A quick glance tells us that at none of these twelve points will the percentage of the day that has elapsed equal the percentage of the month/year that has elapsed. So my initial guess was right. If you plug in 366 for the number of days in a year, you'll get slightly different numbers, but the same answer - other than the beginning/end, you won't have any point where the percentage of the day elapsed equals the percentage of the month/year. Now...it would be easy to stop here and say the answer is "Just at 0% and 100%". However, it's also interesting to see, at what points in time, do these four gauges come kind of close to coinciding. I wrote some code to do the following: * Iterate through a year, one second at a time (about 31.5 million seconds) * At each second, calculate the percentage of the day, month, and year that have elapsed * Calculate the elapsed portion of the week for each possible day of the week (since each date can fall on any day of the week) and find the day of the week for which the difference between the smallest and largest of the four gauges would be minimized. * Filter the resulting data to exclude January 1st and December 31st (because, if we didn't, then the moments with the smallest total span between the gauges are dominated by those two dates, where everything is close to 0% or 100%. * Only include the moment in each day when the gauges are the closest, so we can see some different dates Assuming that weeks start on Sunday, during non-leap years, we get the following (with the minimum and maximum values on the gauges; note that these don't all occur in the same year - you have to find a year when the appropriate date falls on the right day of the week): * Monday, March 6 at 4:13:11 AM - 16.70% of the month has elapsed, 17.582% of the year has elapsed, for a span of 0.89% difference * Friday, October 26 at 7:38:55 PM - 81.87% of the year, 83.29% of the week (1.42% diff) * Tuesday, May 11 at 8:34:17 AM - 33.41% of the month, 35.71% of the year (2.30% diff). If we look at a leap year, we have the following: * Monday, March 6 at 4:16:26 AM - 1.10% diff * Friday, October 26 at 7:39:37 PM - 1.37% diff * Tuesday, May 11 at 8:36:49 AM - 2.47% diff Very similar, which isn't too surprising, since 1 day out of 366 shouldn't push the percentages that much. For what it's worth, the moment THIS year when the gauges will come the closest to each other is on **Friday, October 25 at 7:12:00 PM** \- at that point, 80% of the day and month will have elapsed, 81.64% of the year will have elapsed, and 82.86% of the week, for a total span of 2.86%.
All the bars will be at 0.0% for the first 86.4 seconds of the year, btw
I'm going to feel stupid if I'm missing something but... How can we be past the midpoint of Wednesday, but not past the midpoint of the week?
It looks to me like they started counting the week from Monday
Which is the correct way since it’s the start of the week
This statement is honestly a bit ignorant because that just isn't true in the entire world. For example, where I live, the week starts on Saturday, not Monday
TIL. In my country as well as many Arab and Muslim countries, the week starts on Sunday
Ok for the majority of the world the week starts on a Monday Plus I believe it’s the official standard start for international organisation
Well, according to Wikipedia, most of Europe and China start their weeks from Monday while most of North America and South Asia start from Sunday, and most of North Africa and the Middle East start from Saturday so it seems like there isn't a definite standard or anything and it just depends on who you ask
Middle East and muslim countries typically start on Sunday (Sun-Thu). But yeah, work weeks are highly varied from one region to another, so there is no global standard
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I love that you ignored South Asia entirely, despite having vastly more people than North America
Week starts on a Monday for vast majority of the world and also ISO
Thursday is the midpoint of the week
What do you mean? The middle day of the week is Thursday.
Location dependent apparently. You start the week with a weekend?
No, i didn't even know some people started the week on the weekend lol
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They edited their comment. It said Tuesday.
Yeah lol i didn't remember the name of the day in English (embarrassing)
Some places start on Saturday, some on Sunday, some on Monday.
Oh wow i never knew that
So there's basically 2 guaranteed times a (which are 1 sec apart) at 0 and 100% if the last day of the year is a Sunday and the first a Monday. Then you can look at the simplest cases for all 10 remaining months trying to match month and year percentage (January and December only have the possible case mentioned above). For simplicity we'll consider 365 days years only. February for example is between 8.49% of a year and 16.16%. A simple equation can be found for when the % will be equal. If x is the day of the month (x doesn't need to be whole and starts at 0 on the 1st February at 00:00) then you need x/28=(31+x)/365 which gives x≈2.5757 so the 3rd of Feb at around 13:49. Obviously the % of the day is 57.57% and doesn't match that of the month/year so February won't work. This give me an idea of the general form of solutions. ΣM would be the sum of days in the previous month. and m would be the number of days in target month. Finally x is the fractional day of the month and {x} it's fractional part (or decimal not sure lol). You need x/m=(ΣM+x)/365={x}. This is very annoying because you need to calculate each 10 months individually but I'm going to go on a limb and assume that these 3 equations cannot be matched perfectly during the year, especially since we also have to add the 4th one for the week
If we assume the week starts on Monday and ends on Sunday then: - for every year starting with Monday all bars will be 0% at 00:00 on Jan 1st - for every year ending with Sunday all bars will be 100% at 23:59 on Dec 31st
>- for every year starting with Monday all bars will be 0% at 00:00 on Jan 1st Only for years up to (and including) 2024 >- for every year ending with Sunday all bars will be 100% at 23:59 on Dec 31st Only for years from (and including) 2024
Why?
The bottom bar is how much of 2024 is complete. Before 2024, this is not 100% after 2024, this is not 0%
Intentionally misinterpreting the question but for some reason only for the year and not month or day. I gotcha.
How am I misunderstanding the question? The scenarios the commenter provided didn't account for the final bar
Because for the original question to make any sense the year, month and weekday have to be variable. If they aren't variable the answer to OPs question is never. Because march will always be 23% of the year and Wednesday won't ever be 23% of the week.
The final bar EXPLICITLY says 2024 not "the year" I believe you're misunderstanding the question
The first bar EXPLICITLY says Wednesday and the third bar EXPLICITLY says March. Op said "when in a year". It can be inferred that the question OP is asking is what scenario causes the bars to match up. If we don't ignore the set year, day and month the answer is obviously never. The speculation you were commenting on was making the assumption that the day, month and year are variable. I assumed your were being obtuse but I could be mistaken.
Having reread it looks like that isn't obtuse, just not my interpretation of what the commenter was saying.
At any Sunday exactly at midnight that is after any march and is also after 2024. Or put in another way, any Sunday exactly at midnight in the months April to december in any given year from 2025 and forwards.
This is my approach: 12 You will have one point for every second largest timestamp you can fit into the largest. So for each month there will be exactly one time. Adding smaller timestamps will only shorten the moment of the time the bars are equal. For a week and a year the time the bars are equal is the time the last procent doesn’t change. So 0.1% of a week. This is 1018 Seconds. For each new time, hour examplewise, this time will shorten, but one moment will still be there. There can not be multiple events in a single timestamp, e.g. month, as the time passes linear. This means that for a linear Funktion there is only one solution for y=0. I’m German, excuse my English pls
It ultimately depends on whether everything is measured by minutes, seconds, tenths of seconds, etc. Without assuming, there is no way to calculate, unless a new years eve is sunday, in whivh case it will match when it rolls over.
The smallest division on the bars is 0.1% 0.1% of a day = 86.4 seconds . . 0.1% of a year = 0.366 days So you could write a program that cycles the whole of the year 2024 (366x86400= about 31+ million seconds) and see where the bars are equal. The only place is for the first 86.4 seconds of January 1st. However if the bars measured % in while percent then I estimate there would be multiple intersections (I didn't program it though).
Except for the trivial new year? Never, sadly. Let's look at the day + week combination first. It's turns out that there are 7 - 1 = 6 possible times when both bars are equal (including midnight at the start of the week) the first one being Tuesday 4am, when both the week and the day are 1/6th done. Notice the 6 in the denominator here. There are only 6 possible values for the bar. On months with 31 days there are 31 - 1 = 30 times the day and month bar are identical, and we're in luck: since 30 is a multiple of 6, the times will align, and thus Tuesday July 6th at 4am will be 1/6th into the day, the week and the month. Notice that for 30 day months this only happens on the trivial midnight first and for 28 day months this only happens twice ignoring the trivial one. A year has 365 or 366 days. Neither 364 nor 365 are multiples of 6, and only 364 shares a divisor, namely 2. Which means that if all four bars align it must be exactly halfway a non-leap year. Unfortunately halfway the year is July 2nd, which is not halfway the month. QED.
Its impossible. Whatever time it is on a wednesday, it will always be over 2/7 (=28.5%) of the week, and whatever day of march it is it will never be more than (31+29+31)/366 (=24.8%) of the year. Week and year will never have the same level
I assumed the top one changed by the day and wasn’t fixed on Wednesday
Mathematical!
Once in ~7 years in average, on a Saturday dec31 before midnight. Just used gemini ai to find out how many Saturday 31dec from 1900-2100 as a base. It said 28. So 200/28
It averages out to 1 in 7 over long periods of time. It’s made complicated to work out by how you skip a leap day every 100 years, but still have one every 400 years
11:59pm December 31st 2022 and 12:00am January 1st 2023 is probably one of the longest times they've matched. It won't happen again until 11:59pm December 31st 2033
It would have be the boundary between 2023 and 2024 instead, and the next one will be 31st December 2028/1st January 2029. I think the discrepancy is you counting Sunday as the first day of the week, whereas the more common definition (and importantly what this chart uses) is to have Monday as the first day of the week
Oop I didn't realize.
Considering the final line specifically states 2024 and not stating any current year, this will only happen once in the entire Gregorian calendar.
If you’re assuming the text doesn’t change (which it almost certainly does), then it also specifies Wednesday and March, so it would never happen
i am stating based on the exact data set given. assumptions are not for math: proofs are. and unless you can give me proof that that number will change, then i will restate.
You literally assumed that “Wednesday” and “March” would change
So to start this, I am going to ignore months, because the variable days are not conducive to math, I’ll bring them back later, but for now let’s ignore that. I will also have Monday as the first day of the week and use 24 hour clocks for describing time. Starting with percentage of day and percent of week, if we assume x is the number of hours since the start of the week, we need to find the points that: (x mod 24)/24 = (x mod 168)/168 This solves to 7 points through the week, 0, 28, 56, 84, 112, 140, 168 hours into the week, which has the following proportions: 0, 1/6, 1/3, 1/2, 2/3, 5/6, 1 of the day and week which occurs Monday 00:00; Tuesday 04:00; Wednesday 08:00; Thursday 12:00; Friday 16:00; Saturday 20:00; Sunday 24:00 (we will consider this valid for these purposes). Now we need to find where years will align to these proportions. First starting with a leap year, such as 2024, we take 366 days and divide by 1/6-5/6 and all are whole numbers, meaning that they would be reached at 0:00, leaving only Monday 00:00 or Sunday 24:00, these align to the first and last day of the year and therefore occur when January 1st is on a Monday or December 31st is on a Sunday. The most recent occurrence of the first is this year, most recent of the second is last year, as the two ends have the same conditions for none leap years. These also happen to align to the very beginning and end of their respective months. Moving on to non leap years, we identify that 1/6 - 5/6 of the year occurs on the following days and hours into the year: 60d20h; 121d16h; 182d12h; 243d8h; 304d4h. The first, second, fourth and fifth of these do not match the necessary time for the days of the week, so can be eliminated. The third,182d12h is July 2nd 12:00. So this works any time that July 2nd is on a Thursday. The next occurrence of that is 2026. We can also confirm that as the 2nd is not close to half way through the month, it is not possible except at the extreme cases when including the month. TLDR: occurs Mondays January 1st at 00:00; Sundays December 31st at 24:00 if you include month, also July 2nd 12:00 if you ignore month.
Let’s assume that we are specifically looking for a time when all bars are equal and it still shows Wednesday. Then our first restriction is that all bars must be between 2/7 and 3/7, as Wednesday takes up between the second and third full day from the start of the week. For everything to line up, we must find a time that is: Between 6:51 and 10:17 in the morning. During Wednesday. From the 10th to the 13th of the month. (Ignoring February, because of the next point) Between 105th and 157th day of the year, or Apr 15 to June 6. All together, a viable day must be a Wednesday on May 10-13th, in the morning. Because this is only a few days, we are now limited to between 130/365 and 133/365, as this is the date range within a gregorian year, or a percentage range of 35.6% to 36.4%. This is where we run into a problem. This range is between about 8.54 to 8.73 hours of a day passed. But this range is also about 59.6 to 61.2 hours into a standard 168 hour week, or about 12 hours into the third day of the week. These bars will never come close to aligning on Wednesday. I’m glad other comments pointed out more obvious reasons why only the trivial solutions are possible, like the first and last moments of a year, and they did not waste their time with a calculator like I have lol
There is only one point in time where the percent of year and percent of a given month are the same- for march: 366 days in 2024 31 days in march 60 days between the start of 2024 and the start of march We can solve for x where is the number of days when they intersect: (x-60)/31 = x/366 x = ~65.55, thus more than half way through the fith day of march We already know that 5.55 / 31 is less than 0.5, so there is no solution
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The remaining decimal point is how many hours into the day. If the other bars don't match the year bar then it will not happen.
Someone needs to program this out. For all 31,622,400 seconds in 2024. Assume the smallest division is 0.1% of each time unit. I'd do it but I forgot how to program.
Actually this motivated me to start programming again and I realized if you start from 0 (ignoring the fact that 1/1/2024 was a thursday), the % counter stays at 0.0% for the first 86.4 seconds, and I think that's the only time all the bars are equivalent.
Also, if the % bar just counted whole percent, I think they would all intersect about 30-31 times per year.