MOS: Kaprekar’s Constant, 6174

Let’s talk about Kaprekar’s constant because it’s just fucking neat.

Today’s Moment of Science… 6174.

What do mathematicians do? Well, if you were Dattatreya Ramchandra Kaprekar, probably a lot of rearranging and subtracting. A recreational mathematician from India, Kaprekar was incredibly capable of understanding and describing new classes of numbers. Born in 1905, he had no formal post-graduate training in mathematics, yet was extensively published.

For his contributions, he gets his own number. There are many like it, but this one is his. What’s special about 6174? It’s not so much the destination, it’s the journey there.

Start with any four digit number, as long as two of the digits are different.
I’m going to start with 7295 because that’s just what my fingers hit first.

Then, rearrange the digits into two numbers, one in descending and one in ascending order. If your number has zeros in it, yes zeros can go at the start for the smaller number.
From my number, 7295, I get 9752 and 2579.

Next, subtract the smaller number from the bigger number.
9752-2579 = 7173

Then, repeat the ‘rearrange and subtract’ steps for a while. Eventually, no matter what number you started with, you will land at Kaprekar’s constant, 6174. Fuck it, let’s see how long ‘eventually’ takes us.

7731-1377 = 6354
6543-3456 = 3087
8730-0378 = 8352
8532-2358 = 6174

I just picked a number at random and started banging these into my calculator, and we’re at Kaprekar’s Constant in five calculations. Which is fucking cool.

Why does it work? It’s just how the numbers work out. Try it yourself, or try it out on a friend and freak them out by predicting the number they’ll get stuck at. Because math is at least a bit more fun than you remember.

D.R. Kaprekar was quoted as saying “a drunkard wants to go on drinking wine to remain in that pleasurable state. The same is the case with me in so far as numbers are concerned.” He spent most of his career as a school teacher, passing away in 1986 at the age of 81.

This has been your Moment of Science, taking a moment to drink in the pleasure of it all, for Kaprekar.

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About SciBabe 375 Articles
Yvette d'Entremont, aka SciBabe, is a chemist and writer living in North Hollywood with her roommate, their pack of dogs, and one SciKitten. She bakes a mean gluten free chocolate chip cookie and likes glitter more than is considered healthy for a woman past the age of seven.

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