How good are you at calendar arithmetic?

There are 30 days from April 4 to May 4.
31 days from May 4 to June 4, so there are 71 days from 4/4 to 6/14.

In a leap year, what date is midyear?

I can figure it out,,but it takes me a minute, I’m not super fast at it. I know my birth month is 31 and my parents’ marriage month is 31, but the rest I need a few seconds to do the rhyme to be sure.

@Brian1946 , That is the reasoning that I expected. I wonder how many people would do it that way.

The mathematician John Conway found a nice way of figuring out what day of the week a given date falls on for even numbered months.. The following dates all fall on the same day of the week: last day of February, April 4 (4/4), 6/6, 8/8, 10/10/ 12/12. The case for February is different from the others. Can you come up with a simple argument covering the other cases? As a hint, all months after February alternate between 30 and 31 days, except for July and August.

If you think of it like “borrowing 10” in subtraction:
May 4 = 30 days of April + 4 = April 34 => May 4 – Apr 4 = 34 – 4 = 30 days.

Similarly, Jun 14 = 30 days of April + 31 days of May + 14 = April 75 => Jun 14 – Apr 4 = 75 – 4 = 71 days.

very good at it.

Pretty good. Took me a minute but i can do it in my head.

I like timeanddate.com for any calendrical questions, including computing intervals.

I do remember, though, how many days hath each month. And if I forget, here’s an old trick:

Close your fists and hold them side by side, knuckles up. The knuckle of your left little finger is January. From there, count the knuckles and valleys. The long months are on the knuckles and the short months are in the valleys. July and August, both 31s, come next to each other on the knuckles of the index fingers.

timeanddate fun: “The 18th of April in (17)75”, when Paul Revere took to horse with news, was a Tuesday. Doesn’t that make it seem more real?

Yes, not a problem.

Here is John Conway’s method for determining the day of the week for even numbered months. The following dates all fall on the same day of the week: the last day of February, April 4 (4,4), 6/6, 8/8, 10/10 and 12/12. This is easily verified:

To get from the last day of February to 4/4, we use all 31 days of March plus 4 days in April, giving 31+4 = 35=5×7, which is exactly 5 weeks, so the two dates fall on the same day of the week.

To get from 4/4 to 6/6, we go 30 days from 4/4 to 5/4 then 31 days from 5/4 ti 6/4 and finally 2 days from 6/4 to 6/6. 30+31+2=63=9×7, so the two dates fall on the same day of the week. We apply the exact same logic for 6/4 to 8/4, 8/4 to 10/4 and 10/4 to12/4. This works because the months alternate between 30 and 31 days in length. The only exception is July and August both being 31 days, but this is not a problem because the month that they precede is September, which is an odd numbered month.

The shared day of the week for this year is Friday, and moves up 1 day for every non-leap year and goes up by two days for a leap year.

This ‘skill’ is an example of brain priority-setting. The need to calculate this sort of thing (at least to me) is so infrequent that my mind has never seen any reason to memorize the algorithm. If once in a blue moon I need to know the interval, I can use the internet (or a printed calendar) to figure out.

My brain does memorize important algorithms, like figuring out restaurant tips (15, 18, or 20%) and calculating what time it is in various countries around the world.

@elbanditoroso , If you look at what @Brian1946 wrote, you will see a simple way of counting days between dates.

30 and 70, estimated.

@Brian1946 , The midpont of a leap occurs at midnight of July 2. The wqy I figured this was to compare number of days per month from January to June with days per month from July to December. There were matching pairs of numbers for all months except for February with its 29 days and a month with 31 days from July to December. I had to add a day to the first 6 months and remove a day from the last 6 months, giving the boundary between July 1 and July 2, which occurs at midnight of July 2.