Digital Roots: The Ultimate Mathematical Trick to mess with your mind

dayitva (25)in #mathematics • 7 years ago (edited)

A cool mathematical trick to tell a layman and look super cool

The Magic:

To demonstrate this, you tell them to grab a calculator, multiply random four-digit numbers, and write down the results, but intentionally write some of them wrong. Common mortals wouldn't be able to tell the difference, but you're not a common mortal, so you briefly glance over each problem and tell them which ones were changed.

The Math:

The secret is so ancient that it was already old by the 10th century, and so useful for double-checking your homework that you might have learned it in school and just forgot. Let's take the following problem:

Is that result right or wrong? No clue. Unless, that is, we were to make all those scary numbers more manageable by simply adding up their digits:

Those are the numbers' digital roots -- sort of like the spokesperson of each number that can represent it when it can't be bothered to leave the house. So, instead of multiplying the big four-digit figures, we can multiply the roots instead. If the roots of the question and the answer match, congratulations, the answer is right! If not, then someone's lying or wrong.

This method is called casting out nines, and there's an even bigger mindblow you can pull off with it:

Tell your spectators to take any long number (let's go with 6,969), rearrange it to make another number, and then subtract the smaller number from the larger one (9,966 - 6,969 = 2,997) -- the digital root will always be 9, for some reason. Now instruct them to multiply the result by another figure, as big as they want (say, 8,008,135). Finally, have them choose one digit as their secret number, and give you the others.

They'll be thinking "I just spent half an hour mixing, subtracting, and multiplying random shit. No way you can guess that number." Unless you add up all the digits and subtract the result from 9 (because that's still the root), like this:

Boom, secret number. You can draw some alchemical symbols or something to spruce up the presentation, but I’m guessing it won't be necessary. They'll be scared enough of you as it is.

Footnotes :
http://www.cracked.com/article_21187_5-amazing-wizard-tricks-you-can-do-with-basic-math.html

#maths #tricks #cool #magic