D.R. Kaprekar discovered a number that almost any four-digit number reaches, within 7 steps, through a repeated digit-rearrange-and-subtract process. What is this number, now called Kaprekar's Constant?

6174. 6174 is the answer. Take a four-digit number and arrange its digits to make the largest and smallest numbers. Subtract the smaller from the larger and repeat. Almost every start ends at 6174 within seven steps. The numbers 1729, 3141 and 9999 are not the end point. Memory hook: the routine stops at 6174. Read more: Srinivasa Ramanujan, D.D. Kosambi, Achievements of Indians in Science and Technology.

Which prize did Kaprekar win in 1927 as a student at Fergusson College, Pune?

Wrangler R P Paranjpe Mathematical Prize. The Wrangler R P Paranjpe Mathematical Prize is the answer. It went to the best original mathematics by a student. Kaprekar won it in 1927. The Bhatnagar Prize and the Fields Medal are for established scientists, not students. Kaprekar never won them. Memory hook: a college prize in 1927. Read more: Srinivasa Ramanujan, D.D. Kosambi, Achievements of Indians in Science and Technology.

In which town did Kaprekar teach school from 1929 until he retired in 1962?

Devlali. Devlali is the answer. It is a town very close to Nashik. Kaprekar taught there for his whole career. Dahanu is his birthplace and Thane is where he attended secondary school. Pune is where he studied at Fergusson College. Memory hook: born in Dahanu, taught in Devlali. Read more: Srinivasa Ramanujan, D.D. Kosambi, Achievements of Indians in Science and Technology.

At which meeting did Kaprekar announce his 6174 result in 1949?

The Madras Mathematical Conference. The Madras Mathematical Conference is the answer. Kaprekar had found the pattern earlier, in 1946. He announced it three years later in Madras. MacTutor lists a Scripta Mathematica paper on it after that. Memory hook: found 1946, told Madras 1949. Read more: Srinivasa Ramanujan, D.D. Kosambi, Achievements of Indians in Science and Technology.

What does the Kaprekar routine give when you start with 1111?

0. Zero is the answer. The digits of 1111 are all the same. So the largest and smallest numbers are equal. Their difference is 0. Numbers like this are called repdigits. They are the exceptions to the 6174 rule. Memory hook: equal digits give zero. Read more: Srinivasa Ramanujan, D.D. Kosambi, Achievements of Indians in Science and Technology.

Non-repdigit three-digit numbers reach which fixed point under the Kaprekar routine?

495. 495 is the answer. Three-digit numbers reach it in at most six steps. Repdigits such as 333 are left out. 6174 is the fixed point for four-digit numbers instead. 703 is a Kaprekar number, which is a different idea. Memory hook: 495 for three digits, 6174 for four. Read more: Srinivasa Ramanujan, D.D. Kosambi, Achievements of Indians in Science and Technology.

The square of 703 is 494209, and 494 plus 209 equals 703. What kind of number is 703?

A Kaprekar number. A Kaprekar number is the answer. Its square splits into two parts that add back to the number. Self numbers cannot be made by adding a number to its own digit sum. Harshad numbers divide by their own digit sum. Demlo numbers are named after a railway station. Memory hook: split the square and add. Read more: Srinivasa Ramanujan, D.D. Kosambi, Achievements of Indians in Science and Technology.

Whose Mathematical Games column in Scientific American brought Kaprekar world fame in 1975?

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Whose Mathematical Games column in Scientific American brought Kaprekar world fame in 1975?

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