General MacArthur's Favorite Number Game

by Richard W. O'Donnell in Games Magazine

Visitors, especially young ones, often waited for General Douglas MacArthur to perform a miracle, or at least utter something profound, when they met him. The General could not always live up to his press notices.

So, MacArthur started using a mathematical trick that he described as "the old number 115" as a way to maintain his image, have some fun, and mystify his guests.

Ask your friend to write down the number of month in which he was born. (January is 1, February is 2, and so on).

Turn your back so you cannot see what your friend is jotting down in response to your instructions.   Then have that person write down:

Month of birth (Example February): 2
Double it: 4
Add 5: 9
Multiply by 50: 450
Add friend's age (Example 40): 490
Subtract 365: 125

At this point, ask your friend to call out the total, which in this case, is 125.
In your head, quickly and secretly add 115.
In this example, you will end up with 240.
Then proclaim, "Why, you were born in February and you're 40 years old."

Here's how you did it.   The first number -- and the second if the total is a four-digit number -- will indicate your friend's birth month, once you've added good old 115.   The last two digits will indicate his age.

This trick will work no matter what the age or month of birth because you have good old 115 on your side.   At least, it always did for MacArthur.

Why don't you use some algebra to prove it?
Let m = month and a = age.
Then following the instructions above:
Month of birth: m
Double it: 2m
Add 5: 2m + 5
Multiply by 50: 100m + 250
Add friend's age: 100m + 250 + a
Subtract 365: 100m - 115 + a
Add 115 to get: 100m + a. (The 100 just moves the month over 2 places)

Links:

Math Tricks Page
Math Puzzle Page
Miscellaneous Puzzle Page
Handley Math Home Page