I - What day of the week was June 7, 1912?
Step 1: 4 (for June) plus 7 (for the 7th) equals 11 minus 7 equals 4. (We could have saved ourselves a step and just dismissed the 7 for the 7th as it is an even multiple of 7 and was subtracted out in the next instance. Hold the 4 till step 3.
Step 2: We do not need to subtract the largest multiple of 28 because the year is already a year between 00 and 27, so 12 plus 3 (what we get when we divide 12 by 4) equals 15 plus 1 for the century equals 16. We do not need to subtract anything for the leap year adjustment in January or February because the date is June even though the year is a leap year.) 16 minus 14 (the largest multiple of 7 in 16) is 2.
Step 3: Add the 4 from step 1 and the 2 from step 2 and you get 6, which is a Friday. June 7, 1912, was a Friday.
Now let's find each of the Month, Day, and Year of June 7, 1912, when that one element is missing and the Day of Week is known.
II - What Month was it when the 7th of some month in 1912 fell on a Friday?
Steps 1-3: Going through the basic DOW formula in steps 1-3 using 0 as the Month, we come up with a 2, ( 0 from step 1 plus 2 from step 2) .
Step 4:
We know that the Day of the Week is a Friday, a 6. To go from a 2 to a 6 we need 4, and so the month we are looking for is a 4. We know it is a leap year so the values for January and February are 6 and 2.
The only month our target month can be is June with a value of 4.
III - What was the first Day in June 1912 that fell on a Friday?
Steps 1-3: Going through the basic formula in Steps 1-3 using 0 (?) as the Day, we come up with a 6, i.e., 4 from Step 1 and 2 from Step 2.
Step 4:
We know the Day of the Week is a Friday, a 6. To go from the 6 from steps 1-3 to the 6 for Friday we need 0, which is the first Friday of the Month.
We know there cannot be a Day 0, so we add 7 for the 7th, which is what we know the answer to be.
The 2nd, 3rd, and 4th Fridays, then, are the 14th (7 + 7), the 21st, the 28th.
IV - In what Year after (say) 1909 did June 7th fall on a Friday?
Steps 1 -3: Going through the basic formula for Steps 1-3 using 0 for the full Year value, we get a 4 (i.e., Step 1's 4 plus Step 2's 0).
Step 4:
To go from a 4 to the 6 that we know Friday is yields a 2, the value of the Year we are looking for.
Starting our search with the year, calculating the value for 1909 we get a 5 (9 + 2 + 1 = 12 - 14 = 2), which is not what we are looking for. Stepping forward to the next leap year, 3 years away, adding 1 value for each year and then 2 for the leap year in 1912 we get 1910 is 6, 1911 is 0, and 1912 is a 1/2 (2 really since we are not interested in the January/February value). The 2 is what we are looking for, so the first Year after 1909 that June 7th was a Friday was 1912.
To find the next year after 1912, let's jump to the next leap year four years away by adding 5, and we get 1916 equals 7, which is a 0 after we subtract 7. But the prior year was a 1 since we are in a leap year in 1916 so we have to step forward 2 years to 1918 to find the next year with a value of 2. S0 1912 and 1918 have a value of 2.
V - In what Century did June 7th fall on a Friday in the Year 12?
Steps 1-3: From the basic formula from steps 1-3, using 0 for the Century value, we get a value of 5 (4+7+12+3+?=26-21=5).
Step 4:
We know we want a target of 6 (for Friday) and so to go from the 5 from steps 1-3 to a 6 requires a value of 1, which is the value for the 20th Century (i.e., 1900's), so 1912 is our full Year, which we know is right.
