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The Kaprekar constant , named after the Indian mathematician D.R. Kaprekar , is a number that emerges from a mathematical process performed on four-digit numbers in base 10. The constant is 6174 , and it is achieved through a repetitive process of rearranging the digits of a number to form the largest and smallest possible numbers, then subtracting the smaller number from the larger one.   History The concept of the Kaprekar constant was introduced in 1949 by Dattatreya Ramchandra Kaprekar , a self-taught mathematician from India. Kaprekar was fascinated by numbers and often explored their unique properties. His discovery of the constant made him famous, especially for its simplicity and its surprising behavior across four-digit numbers.   The Process (Illustration) Choose any four-digit number with at least two different digits (e.g., 3524).   Arrange the digits in descending and ascending order to form two four-digit numbers: Largest: 5432 Small...

1. 1729 (The Hardy-Ramanujan Number) Origin : Named after a famous anecdote involving mathematicians G.H. Hardy and Srinivasa Ramanujan . Hardy mentioned to Ramanujan that 1729 seemed like a dull number, to which Ramanujan replied that it is the smallest number expressible as the sum of two cubes in two different ways: 1729 = 1 3 + 1 2 3 = 9 3 + 1 0 3 1729 = 1^3 + 12^3 = 9^3 + 10^3 Magic : It's a prime example of taxicab numbers . 2. 1089 (A Palindrome Phenomenon) Process : Take any three-digit number where the first and last digits differ (e.g., 732). Reverse the digits (e.g., 237). Subtract the smaller number from the larger number: 732 − 237 = 495 732 - 237 = 495 Reverse the result and add it to the original subtraction result: 495 + 594 = 1089 495 + 594 = 1089 Magic : The result is always 1089 1089 , regardless of the starting number. 3. 0.999... (The Infinite Nine Paradox) Magic : 0.999... 0.999... is mathematically proven to be exactly equal to 1 1 : x ...