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Kaprekar Constant

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Joe21®

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Kaprekar Constant

May 25, 2020, 11:38 AM

I had never heard of Kaprekar's Constant until a friend sent it to me. The constant is 6174. Select four digits, all different, such as 9218. Now write the numbers in descending order, high to low, 9821, Next, write the numbers in ascending order, 1289 and subtract from 9821. This number is 8532. Now, repeat as above, 8532 minus e358 equals 6174. And for proof we take 7641 minus 1467 and the answer is 6174.

Four digits selected -- 92i8

9821 - 1289 = 8532
8532 - 2358 = 6174
7641 - 1467 = 6174

The required number of steps to arrive at 6174 will vary with the four digits selected. This just happened to require two steps plus proof.