The math looks right to me…I don’t know where the failed logic begins.

Let’s take a look at what you are asking for.
There are 365 days per year available for work.
There are 52 weeks per year in which you already have 2 days off per week, leaving 261 days available for work.
Since you spend 16 hours each day away from work, you have used up 170 days, leaving only 91 days available.
You spend 30 minutes each day on coffee break which counts for 23 days each year, leaving only 68 days available.
With a 1 hour lunch each day, you used up another 46 days, leaving only 22 days available for work.
You normally spend 2 days per year on sick leave.
This leaves you only 20 days per year available for work.
We are off 5 holidays per year, so your available working time is down to 15 days.
We generously give 14 days vacation per year which leaves only 1 day available for work and I’ll be damned if you are going to take that day off!

For example you subtract 16 hours per day that you’re not working, but you count those same hours again when mentioning 2 weeks vacation, 2 sick days, 2 weekend days per week, etc.

What I’m having trouble with is the coffee break/lunch calculation. 23 days of coffee break time means…1104 half hour coffee breaks. Way more than 1 for each of the 261 days “worked”. Am I missing something?

Of course, if by “coffee breaks” they mean “time spent on the SDMB instead of working”, well yeah, I think that comes out just right.

After this point, the message is assuming that your working days are 24 hours long, since you’re being “criticized” for being away from work. So you should be subtracting all breaks from these 24-hour-long days - but the message doesn’t do that.

This doesn’t follow. If you’re working 91 24-hour days, that’s 2184 hours. 91 half-hours is 45.5 hours. 2184-45.5=2138.5 hours, which is 89.1 days (24 hours long).

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With a 1 hour lunch each day, you used up another 46 days, leaving only 22 days available for work.

It’s a trick, playing on the definition of ‘day’. Most folks surely think of a work day as the length of their typical ‘shift’, while this trick plays fast and loose with it, changing your work days to 24 hours at one point.

What sense does it make to subtract the non-working hours from the day, then recombine them into “days”?

Even allowing that, the following remain:

The 30 minutes a day = 23 days in a year is just wrong. Better to combine the 16 hours, the coffee breaks, and the lunch hour into 17.5 hours of each day.

The “2 days per year” of sick leave are 8-hour days, and should be subtracted at the beginning, from the 8 -hour working days, not the 24-hour days. Same for the holidays and vacation days.

“Properly” done, you get 365-104-2-5-14 = 240 days; subtract 17.5 hours from each day and you get 65 24-hour days being worked. If you take a day off, it’s still only 6.5 hours, so what’s the beef?

And it’s already shot. Actually, you have 261 days available, because a working day isn’t 24 hours; it’s 8 hours. The time you spend at home on a day you actually DID work is irrelevant. “Working day” isn’t every 24 hour period; it’s an 8 hour slice.

Basically, this is where most of your missing time is.

This statement establishes that 1 ‘day’ = 8 hrs. But the rest of it continues to consider a ‘day’ as 24hrs.
Do it with a ‘day’ equal to 8hrs and it works out differently:

This all works fine to establish that there are 261 days available in a year for work.
Now switch to hours with 8 hrs equalling 1 day.
261 ‘days’ = 2088 hrs.

Ignore all of this because we’ve already established that a ‘day’ is equal to only 8 hrs.

Subtract 30 min./day: 261 days x 0.5 hr/day = 130.5 hrs
2088hrs - 130.5 hrs = 1957.5 hrs

I believe most people only get ten days of vacation, not fourteen. Also, you should remove full days for sick leave, vacation, etc. before removing the lunch hours and coffee breaks. Otherwise you’d be counting them twice. So that gives us:

There are 365 days per year available for work 5/7 of which are work days, leaving 260 5/7 (~261) days available for work, or 6264 hours.
Since you spend 16 hours each day away from work, you have used up 4176 hours, leaving only 2088 hours available.
You normally spend 2 days per year on sick leave. This leaves you only 2072 hours per year available for work.
We are off 5 holidays per year, so your available working time is down to 2032 hours.
We generously give 10 days vacation per year which leaves 1952 hours.
You spend 30 minutes each day on coffee break which counts for 122 hours (.5 hours/day * (261 - 2 - 5 - 10)days) each year, leaving only 1830 hours available.
With a 1 hour lunch each day, you used up another 244 hours, leaving only 1586 hours available for work.

Then subtract whatever time you spend trying to figure out how many hours you have to work every year, and that should be your total. Assuming I didn’t screw up the math anywhere.

Try restating the entire thing in fractions, see how it comes out. 2/3 of the time is spent outside work. Of that remaining 1/3, only 5/7 is on weekdays. (5/7)*(1/3)=5/21. Continue that sort of logic and you will get a more sensible answer. Convert between hours and days as needed, but be consistent in your units then.