What is the mathematical explanation for this trick? I found the following method to find one's age. It is working exactly for my case. I like to understand and solve this puzzle. If this is wrong forum, my sincere apologies. Please guide me solve this.


*

*Take last digit of your mobile number 

*Multiply it by 2

*Add 5 with the above answer

*Multiply the answer with 50

*Add 1764 with the answer

*Subtract the your birth year from the result in part 5 (example 1985, 1973, etc.)


Now you will get 3 digit number. The first one is last digit of your mobile number, last two digits are your age.
 A: That's elementary. If $d$ is the last digit and $y$ your birth year, you are computing
$$(2d+1)50+1964-y=100d+2014-y.$$
The first term is the digit shifted two positions to the left (times $100$); the other two terms compute your age.
You'll have to increment the constant $1964$ every year, and the trick won't work for centenarians.
A: *

*Let $n$ be the last digit of your mobile number.

*$2n$

*$2n+5$

*$50(2n+5)=100n+250$

*$100n+250+1764=100n+2014$ (fixed by Daniel R)

*Let $y$ be your year of birth. Then we have $100n+(2014-y)$.


Since $2014-y$ is your age (assumed to be $<100$), the hundreds digit is $n$ and the last two digits are your age.
A: $50(2x + 1) + 1964 - y = 100x + (2014 - y).$
If you were born before August 1st in year y, then (2014 - y) is your age. If you are under 100, then it's a 2-digit number. So the right-hand side of the equation is just a three digit number whose first digit is $x$ (doesn't matter what one-digit number $x$ we started with) and whose last two digits are your age.
edit: fixed lhs as per comments
