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LEVEL 5
Calendar Calculations
The Formula
(Year + LeapYears + Century + Month + Day) mod 7
Year Code
Use the last 2 digits of the year. E.g., for 1985 → use 85.
Leap Years
Divide Year Code by 4, drop the remainder. E.g., 85 ÷ 4 = 21 (keep 21).
Century Code
1900s = 0 | 2000s = 6 | 2100s = 4 | 2200s = 2
Month Code
Look up the month in the table (see below).
Special Rule
For January or February in a LEAP year, subtract 1 from the total.
Final Step
Add all parts and take mod 7. Result 0=Sun, 1=Mon, 2=Tue, 3=Wed, 4=Thu, 5=Fri, 6=Sat.
Month Code Table
JAN
0
FEB
3
MAR
3
APR
6
MAY
1
JUN
4
JUL
6
AUG
2
SEP
5
OCT
0
NOV
3
DEC
5
Memory tip: Use "No March May July" → 0,3,3,6 for Jan–Apr. Or just learn the pattern: pairs 3,3,6,1,4,6,2,5,0,3,5 cycling from Feb.
Example: March 15, 2024
Year code: 24 (last 2 digits of 2024)
Leap years: 24 ÷ 4 = 6
Century: 6 (2000s)
Month (March): 3
Day: 15
Sum: 24 + 6 + 6 + 3 + 15 = 54
54 mod 7 = 5 = Friday ✓
Doomsday Anchors
These date patterns always fall on the same day each year — called the "Doomsday." Use them as shortcuts!
4/4, 6/6, 8/8, 10/10, 12/12
Even month pairs
5/9, 9/5, 7/11, 11/7
Rhyme: "I work 9-5 at 7-11"
Jan 3/4, Feb 28/29
End of Jan/Feb
Last day of Feb
Always Doomsday!