[Bigdaddy]

This sounds like a good job interview question from one of those new, high tech companies. I've seen some like "How many piano tuners are in Chicago?" or "How many gallons of water would fit in the Empire State Building?"

No one could reasonably know the answer, but the interviewer gets a chance to see the applicant's problem solving skills given limited knowledge and time.

So what do we know:
Approximately 1775 Micks have been graded by the major TPGs.
Some of those 1775 are re-grades, so the number of cards is somewhat less than 1775, maybe 10-20% less
Mick is a DP, so there were twice as many of him as most other high #s
Mick has always been highly collected - does this mean that more of his cards survived than the other high #s? or were they more 'well-loved' and therefore wore out faster and more likely to be thrown away? I'd guess that a larger percentage of his cards survived than other high numbers.
There are about 3-4 times more Mantles graded (on PSA) than most other '52s
Lots of 'speculative comments' above: Three in a town of 50,000 folks (would equate to ~19,200 at that rate for the US), only seen one ungraded copy in last few years, etc

The real unknown is the number of ungraded copies. Given the fact that it is a DP and maybe saved at a higher rate than other high #s, I'd guess the number is maybe two - three times the number of graded ones. Let's say 2.5.

So, 1750 * 0.8 (20% regrade) = 1400
1400 (graded) + 1400 * 2.5 (ungraded) = 4900

As time goes on, that number will only grow smaller as some are lost, destroyed by fire, flood, etc. Any copies that are found are already accounted for in the 'ungraded' category. And newly graded ones will just go from ungraded to graded, giving us better information on how many exist.

Of course, if you subscribe to the 'Wisdom of Crowds', then just have everyone give an estimate and average the numbers (taking out any obvious outliers).