I - ISO DoW: What Day of the Week) was February 28, 1900?
Step 1 - Add the month value (3) to the day (28) and you get 31. Since 31 is grater than 6, take out the largest multiple of 7 in it (28) and you're left with 3. (I could have ignored the 28 for the day and saved time because why add some known multiple of 7 when I know I will be subtracting it immediately.)
Step 1 - Add the month value (3) to the day (28) and you get 31. Since 31 is grater than 6, take out the largest multiple of 7 in it (28) and you're left with 3. (I could have ignored the 28 for the day and saved time because why add some known multiple of 7 when I know I will be subtracting it immediately.)
Step 2 - Since 00 is less than 28, I do not have to subtract the largest multiple of 28 in it. So I add the 00 to 0 (which is 00/4 is) and add 1 for the century to get 1. I do not subtract out 1 for a January/February month in a leap year because 1900 is not a leap year. Why?
Step 3 - Add the 3 from step 1 and the 1 from step 3 to get 4, which is a Wednesday.
II - ISO Month: In what Month(s) in 1900 was the 28th of the month on a Wednesday?
Step 1: Since we are looking for the Month, the result from Step 1 is only the day, 28, which is 0 (i.e., 28-28=0).
Step 2: 00 + 0 + 1 -1 = 1 (see step 2 for the ISO DoW, above)
Step 3: 0 + 1 = 1
Step 4: We have a 1 from steps 1-3 and we are looking to go to a 4, a Wednesday. 4 - 1 = 3, so the months we are looking for have a value of 3 in a non-leap year. Those months are: February, March and November.
III - ISO Day: On what Day did the 4th Wednesday in February fall on in 1900?
Step 1: Since we are looking for the Day, the result from step 1 is the value for the month of February, 3.
Step 2: 0 + 0 + 1 - 1 = 1 (See step 2 in ISO DoW, above)
Step 3: 3 + 1 = 4.
Step 4: We have a 4 from step 3 and are looking to go to a 4 for Wednesday. So we subtract 4 from 4 and get 0. But since we are looking for the Day, and know that there is no zero day, we add 7. So the first Day of that month that fell on a Wednesday was the 7th. Add 7, 14, and 21 for the 2nd, 3rd and 4th Wednesdays and you get the 14th, 21st and 28th. Our answer, then, is February 28th, 1900.
IV - ISO Year: In what Year in or after (say) 1901 did February 28th fall on a Wednesday?
Step 1: 3 + 28 = 31 - 28 = 3 (see Step 1 in ISO DoW.)
Step 2: We are looking for the year value so this is zero or omitted.
Step 3: 3 + 0 = 3.
Step 4: We have a 3 from step 3 and we are looking for a 4 [Wednesday], so the difference 4 - 3 = 1 is the value of the year we are looking for.
Since we agreed to start in 1901, let's compute the value for that year first. Doing step 3 for 1901 we get 01 [the year] - 0 [which is 01/4] +1 [for the century] - 0 [remember, no adjustment for Jan/Feb] equals 2. Now we can move forward by the crawl method, walk method or jump method. But wait, since we are only one value away from our desired target, why can't we go back a year to look for our target year? We can, and in this case, we subtract 1 year and one value to get 1900 and 1, which is the year we are looking for. If 1900 had been a true leap year, we would have subtracted either 1 or 2 depending upon whether we had already accommodated the extra day for the leap year adjustment, but 1900 was not a leap year so we do not worry about it.
V - ISO Century: In what Century was the 28th of February in year '00 a Wednesday?
Step 1: 28 + 3 = 31 - 28 = 3 (see ISO DoW step 1)
Step 2: Since we do not know the Century the result here is 0 + 0 + ? + ? = 0 (FYI, we used a ? for the adjustment of minus 1 for Jan/Feb in a leap year because if the century is 1600 or 2000, it could be a leap year.)
Step 3: 3 + 0 = 3.
Step 4: We have a 3 and we are going for a 4 [Wednesday], so 4 - 3 = 1. The various century values are 6 for 1600/2000 [Why 6 and why not 0? Because they are leap years and we need to adjust here for the -1 leap year adjustment for January/February], and 5 for 1700/2100, 3 for 1800/2200, and 1 for 1900/2300. So our answer is 1900s.
