The four digit number - 6174 is known as Kaprekar's constant.
Take any four digits with at least two different numbers.
Arrange them into the highest number and the lowest number.
Subtract the lower number from the higher number.
Using the difference, repeat the process.
You will always eventually wind up at 6174.
Example:
9445
9544 - 4459 = 5085
8550 - 0558 = 7992
9972 - 2799 = 7173
7731 - 1377 = 6354
6543 - 3456 = 3087
8730 - 0378 = 8352
8532 - 2358 = 6174
And the 6174 will repeat.
7641 - 1467 = 6174
Try it!
John
Friday, October 04, 2024
Kaprekar's Constant
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2 comments:
A couple of my long time followers will remember It's a Numeric Life.
I thought of her when posting this one.
We want Numeric Life to come back!
https://en.wikipedia.org/wiki/6174
6174 is a 7-smooth number, i.e. none of its prime factors are greater than 7.
6174 can be written as the sum of the first three powers of 18:
183 + 182 + 181 = 5832 + 324 + 18 = 6174, and coincidentally, 6 + 1 + 7 + 4 = 18.
The sum of squares of the prime factors of 6174 is a square:
22 + 32 + 32 + 72 + 72 + 72 = 4 + 9 + 9 + 49 + 49 + 49 = 169 = 132
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