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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.


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Last Updated: January 12th, 2010.