Problem Solved!

One of the 48 new crappy old book I've acquired recently is the New American Encyclopedia of Social and Commercial Information: A Practical and Educational Compendium Suited to the Needs of Everyday Life (James E. Homans, ed. P.F. Collier & Son, New York. 1908).

This book is amazing! It begins

A practical education is the greatest wealth that man or woman may possess. It is a property that cannot be alienated, yet one that may be shared with others without loss. Education is the legacy good parents must bequeath to their children. It is an investment that all young people must be persuaded to seek. Some part of every day should be devoted to the acquirement of a little more useful knowledge.  

I couldn't agree more!  And this crappy old book is just exactly the sort of book to look to for the "acquirement of a little more useful knowledge." It's got everything for everyone.

This is page 1 of the two-page contents

 As I was searching for the acquirement of a spot of knowledge today, I ran across a puzzle in the "Arithmetical Amusements" section: A sure Way to Learn a Person's Age. (Some of the writing in the Encyclopedia of Everything is rather long-winded. I'll just give you the gist of the puzzle.)

Think of the number corresponding to the month of your birth.

Multiply that by 2.

Add 5.

Multiply by 50.

Add your age.

Subtract 365.

Add 115.

Let's say you played along, and you are a 30 year old born in March. Your answer will be 330. If you are 42 years old and were born in October, the answer will be 1042.

What's the trick?

Look at the order of operations. Subtract 365, and then add 115 is a giveaway. 250. Go looking for 250.

My thought train:

Multiplying by 2 makes every number even. Adding 5 makes every number odd. Multiplying by 50 moves the birth month to the 100th's or 1000th's space, always ending in 50.
~~

When trying to figure out a trick, the best first pass is to recreate the trick in the simplest possible terms. 



Suppose a one-year old, born on January 1:

1 x 2 +5 x 50 + 1 -250.

101.

I'm still looking for 250. 

That got me knowing what I already knew, 250 was key. So re-write

x is your birth month. y is your age.

(((2x + 5)50)+y)-250 =xy

Simple math.   

100x + 250 + y - 250 = xy

 330.

You were born in March and you're 30 years old.

No body cares about simple math.