Sunday, April 20, 2008

Mental Bathroom Math

Let me precede this by saying that I'm sure that billions of people have already realized this, and I'm probably late to the game by not doing so.  I'm only posting this for the 12 people that never realized that you could do this.

Everybody knows the following: 

(x+y)(x-y) = x^2 - y^2

Now, this fact makes a simple "trick" possible.  If you have 2 numbers equidistant from a value whose square you know, you can easily multiply them together.

Say you want to multiply 24 and 26.  Set 25 as X, and recall that 25^2 = 625.  Since you chose 25 for X, Y is 1.  The final answer is 624.  That's something that you can do in your head.  It works for everything, and it makes it a little easier to have instant answers for more math inquiries.

Let's stress again that this isn't just for values 2 apart.  62*78 would have an X of 70 and a Y of 8, so you'd have 4900-64=4836 as an answer, something that isn't obviously prone (to an observer) to any trick at all.  Similarly, 109*113 would be 12321-4=12317.

2 comments:

mark said...

Unlike other conjectures you may have posited in the past, this one is mathematically sound. Congrats!

Anonymous said...

Reminds me of a neat video of Professor Benjamin from Harvey Mudd:
http://www.ted.com/index.php/talks/view/id/199