Dattatreya Ramchandra Kaprekar (; 17 January 1905 – 1986) was an Indian recreational mathematician who described several classes of natural numbers including the Kaprekar, harshad and self numbers and discovered the Kaprekar's constant, named after him. Despite having no formal postgraduate training and working as a schoolteacher, he published extensively and became well known in recreational mathematics circles. Biography Kaprekar received his secondary school education in Thane and studied at Cotton College in Guwahati. In 1927, he won the Wrangler R. P. Paranjpe Mathematical Prize for an original piece of work in mathematics. He attended the University of Mumbai, receiving his bachelor's degree in 1929. Having never received any formal postgraduate training, for his entire career (1930–1962) he was a schoolteacher at the government junior school in Devlali Maharashtra, India. Cycling from place to place he also tutored private students with unconventional methods, cheerfully sitting by a river and "thinking of theorems". He published extensively, writing about such topics as recurring decimals, magic squares, and integers with special properties. He is also known as "Ganitanand". Discoveries Working largely alone, Kaprekar discovered a number of results in number theory and described various properties of numbers. In addition to the Kaprekar's constant and the Kaprekar numbers which were named after him, he also described self numbers or Devlali numbers, the harshad numbers and Demlo numbers. He also constructed certain types of magic squares related to the Copernicus magic square. Initially his ideas were not taken seriously by Indian mathematicians, and his results were published largely in low-level mathematics journals or privately published, but international fame arrived when Martin Gardner wrote about Kaprekar in his March 1975 column of Mathematical Games for Scientific American. Today his name is well-known and many other mathematicians have pursued the study of the properties he discovered. Kaprekar's constant In 1949, Kaprekar discovered an interesting property of the number 6174, which was subsequently named the Kaprekar constant. He showed that 6174 is reached in the end as one repeatedly subtracts the highest and lowest numbers that can be constructed from a set of four digits that are not all identical. Thus, starting with 1234, we have: 4321 − 1234 = 3087, then 8730 − 0378 = 8352, and 8532 − 2358 = 6174. Repeating from this point onward leaves the same number (7641 − 1467 = 6174). In general, when the operation converges it does so in at