Beauty In Math – Kaprekar’s Constant

6174

6174 is a special number now known as Kaprekar’s constant – after the great Indian mathematician D.R. Kaprekar who discovered this constant in 1949.  Kaprekar showed that 6174 is the limit attained as one repeatedly subtracts the highest and lowest numbers that can be constructed from a set of four digits that are not all identical.

Let’s try two examples.

First we’ll select the number 5379.  Composing the largest possible number from its four digits and then the smallest and subtracting gets us to 6174 in one step.

9753 – 3579  =  6174

Next we’ll try 4563.  It takes a couple of turns of the crank but we get to Kaprekar’s constant.  Pretty neat for a guy working in the days before electronic calculators.

6543 – 3456 = 3087

8730 – 0378 = 8352

8532 – 2358 = 6174

Kaprikar’s Constant

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