# 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.

1. Take last digit of your mobile number
2. Multiply it by 2
4. Multiply the answer with 50
6. 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.

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## migrated from mathematica.stackexchange.comAug 1 '14 at 17:36

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What year is meant in 6., which is the only point where your age might sneak in. – mvw Aug 1 '14 at 17:40
Should step 3 be "Add 1 to the above answer"? – Daniel R Aug 1 '14 at 17:41
Then I'm puzzled. How does it work for your age? Or should step 5 be changed to "add 1764 to the answer"? – Daniel R Aug 1 '14 at 17:55
Old trick. Back in the day, when mobile devices didn't exist, we had to choose a number between 0 and 9. How how times have changed... – bobthechemist Aug 1 '14 at 23:44
Won't work for anyone above the age of 99. – G. Bach Aug 2 '14 at 20:43

1. Let $n$ be the last digit of your mobile number.
2. $2n$
3. $2n+5$
4. $50(2n+5)=100n+250$
5. $100n+250+1764=100n+2014$ (fixed by Daniel R)
6. 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.

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And this assume this trick is performed in the year 2014. – Derek 朕會功夫 Aug 2 '14 at 1:16
" 2014−y is your age" -- except that it isn't, since I haven't had my birthday yet this year. But, you know, maths is nearly psychic. – Steve Jessop Aug 2 '14 at 11:42

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.

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This answer is also correct. Thanks @Yves Daoust – rajakvk Aug 1 '14 at 18:10
It's obviously correct, but how are you getting (2d+1)50 + 1964 from what is stated? I get that you can rearrange (2d+5)50 + 1764 that way, but that seems like extra work. So I assume you get it some other way. – trlkly Aug 2 '14 at 12:08
@trlkly: the original text was different. – Yves Daoust Aug 3 '14 at 9:20

$50(2x + 1) + 1964 - y = 100x + (2014 - y).$

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

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This is not true as written; you need $(2x + 1)$ for this to work – Omnomnomnom Aug 1 '14 at 17:45
It's obviously correct, but how are you getting 50(2x+1) + 1964 from what is stated? I get that you can rearrange 50(2x+5) + 1764 that way, but that seems like extra work. So I assume you get it some other way. – trlkly Aug 2 '14 at 12:10
the question appears to have been edited to change the number since i made my answer. – hunter Aug 2 '14 at 12:15
@hunter Thanks. Next time, though, I would prefer it if you use the @username notation when you leave a reply to me. That way, the reply appears in my inbox. I only happened to see that this question in the "Hot Questions" part or I would have missed your reply. – trlkly Aug 3 '14 at 3:45
hunter, my bad, yes I edited question. @trlkly sorry for the confusion. – rajakvk Aug 5 '14 at 12:27