Saturday, May 22, 2010

Number Trick

Take the a number x and multiply that by 2; add 5; multiply by 50. If you've already had your birthday this year, add 1760; if not, add 1759. Subtract your four-digit birth year. You should end up with a three-digit number -- the first of which is the number you started out with and the next two are your age.

How it works

Start with the number x.  Multipy by 2, add 5 and multiply by 50.

(2x + 5) * 50
100x + 250

Now we've already multipled the first number by 100, shifting it over by two digits.

Now we just need to get your age into the last two digits.

If y is your birth year, then your age a is

a = 2010 - y

What we want for the final answer is:

100x + (2010 - y)

but we need to get rid of the 250 we already have:

[100x + 250] + [(2010 - y)  - 250]

The first square brackets is what we have so far and the second square brackets are what we want to add.

2010 - y - 250 = 1760 - y

So, finally,

[100x + 250] + 1760 - y

The last part puts your age into the last two digits.

Putting that all together.

(2x + 5) * 50 + 1760 - y