My friend Norma asked me a question last night via Facebook. For practical purposes, I am rephrasing her question as:
Why is the sum of the person's two-digit birth year and that person's age plus one always equal to 111?
Norma, who is now 34, was born in '76. She observed that 76 + 34 + 1 = 111.
I thought of Matty. He was born in '83. Last year, he turned 27. Observe that 85 + 25 + 1 = 111.
My student Alisha, who was born in '96, celebrated her 14th birthday last year. Well, 96 + 14 + 1 = 111.
"So why does this work?," Norma insisted.
Readers, what do you think?
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SOLUTION:
When you say your birth year is 76, you actually mean 1976, which is 1900 + 76.
So if your birth year is X, then it is actually (1900 + X).
If you were born in the year (1900 + X), then in the year 2010, your age was [2010 - (1900 + X)] years old.
So your birth year plus your age plus one
= X + [2010 - (1900 + X)] + 1
= X + 2010 - 1900 - X + 1
= 111.
It doesn't matter how old the person is, the result will always be 111.
Norma's question reminded me of a similar problem. Last December, in a statewide conference I attended in Dallas, the following question (that I also rephrased) was raised for us to play with:
Add your age by the end of this year to the year you were born. What do you get?
Now your turn. Prove why it works.
I wake up to this view from my apartment window everyday for a year now. 
