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A few months ago, I was sitting around bored on my computer, when my dad forwarded me an email. The email contained a link to a mathematics puzzler. For those of you too afraid to click the link, or who simply don't want to, the trick goes as follows:
1) Have a volunteer write down a three or more digit number, with the stipulation that the number should contain at least 2 different kinds of digits (i.e. numbers like 333 are not allowed). Make sure they don't show you this or the following two numbers.
2) Now, have them create a second number by rearranging digits from the first number. (i.e. if their number was 8745, their second number could be 7854, or 4785).
3) Have them create a third number by subtracting the 2 numbers from each other (bigger from smaller generally, although this does not actually matter).
4) From this third number, have them circle one of the digits (but don't circle a zero, as those are already a circle ;-P). Now, have the volunteer tell you all of the digits except for the circled digit. Done correctly, you will be able to tell them what their circled digit is correctly, every time, in a matter of seconds.
How does this work? Read on for more!
1) Have a volunteer write down a three or more digit number, with the stipulation that the number should contain at least 2 different kinds of digits (i.e. numbers like 333 are not allowed). Make sure they don't show you this or the following two numbers.
2) Now, have them create a second number by rearranging digits from the first number. (i.e. if their number was 8745, their second number could be 7854, or 4785).
3) Have them create a third number by subtracting the 2 numbers from each other (bigger from smaller generally, although this does not actually matter).
4) From this third number, have them circle one of the digits (but don't circle a zero, as those are already a circle ;-P). Now, have the volunteer tell you all of the digits except for the circled digit. Done correctly, you will be able to tell them what their circled digit is correctly, every time, in a matter of seconds.
How does this work? Read on for more!
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Signing UpStep 1The Additive Digitial Root
The ability to perform this trick relies heavily upon an obscure mathematical concept known as additive digital roots. Historically, digital roots were used as a type of checksum to catch errors from mental and pencil-and-paper math methods in the dark and forgotten age before calculators.
The additive digital root of a number can be computed by adding all of the digits of a number together to produce a second number, then adding all the digits of that number together, and recursively adding all the digits of a given sum until only a single digit remains. This digit is the digital root of a given number. For more details about using and computing digital roots, check out my instructable on the topic.
By plotting the digital root of a number, a more precise definition of the digital root can be obtained. The digital root is 0 if the number is 0, 9 when the number is 9, the number mod 9 when the number is not a multiple of 9, and 9 when the number is a multiple of 9. This, coupled with the fact that digital_root(x-y) = (x-y)mod9 will allow the math guru to read the mind of his unsuspecting volunteer.
The additive digital root of a number can be computed by adding all of the digits of a number together to produce a second number, then adding all the digits of that number together, and recursively adding all the digits of a given sum until only a single digit remains. This digit is the digital root of a given number. For more details about using and computing digital roots, check out my instructable on the topic.
By plotting the digital root of a number, a more precise definition of the digital root can be obtained. The digital root is 0 if the number is 0, 9 when the number is 9, the number mod 9 when the number is not a multiple of 9, and 9 when the number is a multiple of 9. This, coupled with the fact that digital_root(x-y) = (x-y)mod9 will allow the math guru to read the mind of his unsuspecting volunteer.
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Sorry for the longwinded explanation, but hopefully that makes since.