what is special about 6174?
Yesterday, my son sent me a link to the Mysterious 6174. What's so mysterious? It turns out that 6174 is always the result of Kaprekar's operation. Say what? (That was my reaction...) Read the link for a complete explanation, or see below for an example of Kaprekar's operation in action.
Choose a four digit number where all the digits are NOT the same (i.e., NOT 1111, 2222, etc.) Rearrange the digits to get the largest and smallest numbers those digits can make, then subtract the smallest number from the largest to get a new number. Perform the same operation on the resulting number, and continue. Eventually, you will end up with 6174. At which point, if you continue the operation, you'll continue to get 6174 for the answer.
Here's an example, using 2007 as the starting point:
largest .... 7200 ... 7731 ... 6543 ... 8730 ... 8532 ... 7641
smallest... 0027 ... 1377 ... 3456 ... 0378 ... 2358 ... 1467
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result ...... 7173 ... 6354 ... 3087 ... 8352 ... 6174!... 6174 (again!)
How's that for something to wow 'em at a party. (Um, guess it depends what circles you run in...)
Is there a Kaprekar's number in another base? Different number of digits? What are the limits of this kind of fun?
Start with any 3-digit number (say 245)
form the mirror (say 542)
subtract the larger from the smallr of these two (542 - 245 = 297)
Add the difference and its mirror (297 + 792)
And, tada, the answer is 1089. Every time.
Caution: This bet requires that there be at least one person at the bar who can be trusted to do simple arithmetic :)