Ultra-basic idea...
Pick a year, then
do some math to find
a day-of-the-week.

That's our "Doomsday".

Each month of that
year has a date we
can reference as the
same day-of-the-week
as that "Doomsday".
The base "century part" of 2016 is 2000
The "year part" of 2016 is 16

The base-doomsday for century 2000 is 2 (from Table X)

Now, complete this sum:
baseDoomsday+year+round( year ÷ 4 )=
2+16+round( 16 ÷ 4 )=
2+16+round( 4 )=
2+16+4= 22

Now divide that total by 7 and get the remainder...
total÷7 =        
22÷7 = 3 with remainder 1
This remainder, 1, is the Doomsday for 2016. Day 1 is Monday (from Table Y).

So now we must see what date, in our month (Feb 2016), is a "Doomsday Monday".
The doomsdate in month 2 (Feb) is 2/29 (from Table Z).
Remember that on a leap year:
  • January's Doomsdate is the "32nd" (just pretend for now, ok?)
  • February's Doomsdate is (still) the last day of the month (Now the 29th).
  • And now we know that 2/29/2016 was a Monday!

    And 2/22/2016 was also a Monday
    And 2/15/2016 was also a Monday
    And 2/8/2016 was also a Monday
    So...
    2/9/2016 was a Tuesday

    TABLE X
    base
    centuries
    base
    doomsday
    1500190023003
    1600200024002
    1700210025000
    1800220026005
    * You probably only need to
    remember the red years!
    TABLE Y
    week dayday num
    Sun0
    Mon1
    Tue2
    Wed3
    Thu4
    Fri5
    Sat6
    TABLE Z
    MonthDoomsdate
    JanJan 31st (or Jan "32nd" in leap years)
    FebFeb 28th (or Feb 29th in leap years)
    MarMar "0th"
    Other odd#
    months
    4/4, 6/6, 8/8,
    10/10, and 12/12
    Other even#
    months
    5/9, 7/11, 9/5, and 11/7
    (Remember: "I work 9-to-5 at the 7-11")