Hans Fugal wrote:

> 	Iterating this sum-of-squared-digits map always eventually
> 	reaches one of the 10 numbers 0, 1, 4, 16, 20, 37, 42, 58, 89,
> 	or 145 (Sloane's A039943; Porges 1945).

As long as we're noting strategy, the site also noted that 16 and 61 are 
identical in terms of the next number.  Any set of digits can be 
scrambled any which way and it won't matter.  61 will eventually work 
around to 16 also.   (As shown by the proof of 3, earlier.)

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