## Friday, June 21, 2013

### Indian Math Trick

A few days ago my son excitedly rushed to show me a trick he learned via Facebook. It was called an Indian Math Trick probably because Indians are very good and confident at math and you have to be both to do the tricks.

Here is the trick:
Take two large two-digit numbers, for example 97 and  86.  It is a pain to multiply them without calculator, right?
Computers do it easily: 97 x 86 = 8342
Can someone human to do it in his/her head?
Turns out anyone can:
Take complements of these numbers that bring each to 100: for 97 it will be 3, for 86 it is 14.
Multiply these compliments and you get the last two digits in your desired result: 3 x 14 = 42
Now add these two compliments: 3+14=17    Subtract this number from a 100 and you will get the first two digits in your number: 100-17=83
8342

Pretty impressive!
Now, tell me why it works and when?

Image is by Partha Sarathi Sahana distributed under CCL.

Your answers are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

Anonymous said...

Quick correction, it's "complements" not "compliments."

Maria said...

Thanks - corrected!

Magic Kid said...

100-17 is 83 not 86. Also it is easier to just take the complement of one of the numbers as in the complement of 97 is 3 and subtract that from the other number as in 86-3=83.

Magic Kid said...

Also it works the same way as multiplying (100-3)(100-14) where you get 10000-1700+42......but you are waiting to multiply by 100 until you have done the subtraction.

Larry Krakauer said...

It works as described as long as the product of the complements is only two digits. If the original numbers are x and y, then:
(100-x)(100-y)
= (100)(100)-100x-100y+xy
= 100[100-(x+y)] + xy

So as long as xy doesn't carry out of the two least-significant digits, xy gives those digits, and 100-(x+y) gives everything shifted two places to the left.

Anonymous said...

Here is how it works. http://www.topbananaeducation.org/content/indian-math-trick-response-math-mom

Maria said...

I know this was not trivial and required a bit of experience dealing with such kind of "magic". Cheers to all who entangled it - Magic Kid, Larry and Alex that we will call Top Banana:)

Larry and the Magic Kid described the general case expressing two numbers through their complements to 100
(100-x) and (100-y)
as 97 is (100-3) and 86 is (100-14)

then he showed that the result has x times y in the lowest digits and (100-(x+y)) in the highest.

3x14=42
100-(3+14) = 100-17 = 83
append them and get 8342
Whoa-la!

Top Banana generalized even further showing how to do this with any reference and not only 100.

I wonder if any of you is Indian:)
see you all next week!

Anonymous said...

It's no magic or trick. Just pure Vedic Maths. Based on some sound reasoning and nifty use of associative and commutative laws. For more fun such as this, Google "Vedic Maths", plenty of sites and plenty more fun