495 (number) explained

495 (four hundred [and] ninety-five) is the natural number following 494 and preceding 496.

Mathematics

The Kaprekar's routine algorithm is defined as follows for three-digit numbers:

1. Take any three-digit number, other than repdigits such as 111. Leading zeros are allowed.
2. Arrange the digits in descending and then in ascending order to get two three-digit numbers, adding leading zeros if necessary.
3. Subtract the smaller number from the bigger number.
4. Go back to step 2 and repeat.

Repeating this process will always reach 495 in a few steps. Once 495 is reached, the process stops because 954 – 459 = 495.

The number 6174 has the same property for the four-digit numbers, albeit has a much greater percentage of workable numbers.^[1]

See also

• Collatz conjecture — sequence of unarranged-digit numbers always ends with the number 1.

References

• Eldridge. Klaus E. . Sagong, Seok. The Determination of Kaprekar Convergence and Loop Convergence of All Three-Digit Numbers . The American Mathematical Monthly. 95. 2. February 1988. 105–112. 10.2307/2323062. The American Mathematical Monthly, Vol. 95, No. 2. 2323062.

Notes and References

1. [Kaprekar's routine#CITEREFHanover2017|Hanover 2017]