Puzzlet 66 - The Answer

PUZZLET 066

The Kapreakar Process

Find all 3-digit primes which take just 6 steps in the Kaprekar Process (see below) to reach 495.

The Kaprekar Process must always begin with a 3-digit integer and will always terminate with the same number, 495. For example, take 323:

1.

2.

3.

4.
5.

Sort its digits into ascending order, calling this A. So A = 233.

Take the reverse of A and call it B, so that
B = 332.

Subtract the smaller from the larger number, giving B - A = 99. Call this 099 to preserve the 3-digit format.
Repeat the process, giving 990 - 099 = 891.
Keep on repeating, giving the series 323, 099, 891, 792, 693, 594, 495.

As predicted, the series terminated with 495. It always does, regardless of which 3-digit integer you start with.

In this Puzzlet, you must always start with a prime number. The challenge is to find those 3-digit primes which complete the sequence in exactly 6 moves.