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MATH VANITY
Posted on 10/20/2003 2:20:00 PM PDT by Publius6961
Request to all technical dweebs out there primarily mathematicians and number theorists about why the following is always true.
Start with a 3 or 4 digit number.
Scramble the same digits to create a new number.
Subtract the smaller number from the larger number.
Add all the digits in the answer as many times as necessary to get a single digit.
Why does this always work?
TOPICS: Chit/Chat; Conspiracy; Education; Hobbies; Humor; Miscellaneous
KEYWORDS: math; pain; puzzle; toomuchtime
Any help is appreciated
To: Publius6961
it works for the same reason that if you transpose two numbers when you are adding or subtracting them, the error will always be divisible by 9.
To: Publius6961
321-123=198 ?
3
posted on
10/20/2003 3:00:14 PM PDT
by
muskogee
To: Publius6961
I assume you mean the single digit is always equal to 9.
When you add the digits of a number repeatedly until there is a single digit, it is call the digital root of that number. The digital root of a number is the value of the remainder when you divide a number by 9. Assume you have 2 numbers A and B. Subtract B from A and get the result C. The digital root of A minus the digital root of B should equal the digital root of C.
By scrambling the same digits, what you have is two numbers with the same digital root. By subtracting the numbers the result will be a number with the digital root of zero. There is only two single digit numbers that have a digital root of zero, 0 and 9. By scrambling the digits of the original number will result in a number greater than 0 and of course if the number is greater than zero then sum of the digits will be greater than zero, which means the result will alway be 9.
You may remember a trick that was taught in grade school to tell if a number is divisible by 9; add the digits together and if the result is divisible by 9 then so is the number. Same trick works for numbers divisible by 3. Same principle.
4
posted on
10/20/2003 3:45:16 PM PDT
by
ned_budge
To: muskogee
321-123=198 ? 1+9+8 = 18
1+8 = 9
5
posted on
10/20/2003 5:03:23 PM PDT
by
Publius6961
(40% of Californians are as dumb as a sack of rocks.)
To: ned_budge
Thank you. Best explanation I've received yet.
I have to look more into this digital root business; if I ever learned it, I sure don't remember.
Is it easier than the first derivative of the transcendental functions?
6
posted on
10/20/2003 5:09:16 PM PDT
by
Publius6961
(40% of Californians are as dumb as a sack of rocks.)
To: Publius6961
Thanks to all who answered this question.
For those who are curious to know more, I found the following link educational and, well, topical.
Enjoy.
http://www.rain.org/~mkummel/stumpers/27oct00a.html
7
posted on
10/20/2003 8:13:38 PM PDT
by
Publius6961
(40% of Californians are as dumb as a sack of rocks.)
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