Robert Belanger (28 May 2011)
"The Sum is Always 111"

There is nothing significant, or magical, about the 111 sum of a person’s age in 2011 and the last two digits of their birth year. The intent of this message is to show why this statement is true.
 
The diagram below is a graphical representation of the idea expressed in “Take the last two digits of your birth year, add your age in 2011 and the sum for everyone is 111.”
 
Step 1.  Taking the last two digits of your birth year is the same as subtracting 1900 from your birth year (assuming you were born after 1900. We can call this number of years since 1900, x, which represents algebraically the value for any person born since 1900.
 
(Of course the total number of years between 1900 and 2011 is exactly 111 for everyone and is not a variable. If the relationship were for 2012 the constant value would be 112 instead of 111. In general, any year minus 1900 is the constant replacing 111 for other years.)
 
Step 2.  The age of a person in 2011 will be the number of years since 1900 minus x, the last two digits of the birth year.
 
1900                    (Birth Year – 1900)              2011
                x
             (111 – x)
0                                                                            111
   
Numerical Example:

For example, if a person were born in 1975 the age of the person in 2011 would be 36, i.e., (111 – x) or (111 – 75) or 36.
 
1900                    (1975 – 1900)                     2011
                75
             (111 – 75)= 36
0                                                                           111
 
General Summary for 2011:
 
The whole length = 2011 – 1900 = 111
The birthday length = Birth Year – 1900 = x
The age in year 2011 = (111 – x)

The sum of a person's age (e.g., 36) in 2011 plus the last two digits of the person's birth year (e.g., 1975 - 1900 = 75) equals 111 for 2011 (i.e., 36 + 75 = 111).
 
2011 Formula for Total Length of Line in Diagram = x + (111 – x) = 111