Hofstadter's Metamagical Themas contends that there are 2 solutions.

Oddly enough, I came across a similar problem in a Lewis Carrol puzzle book. It was phrased as follows:

_____________________
|0|1|2|3|4|5|6|7|8|9|
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|_|_|_|_|_|_|_|_|_|_|
[download]

The trick was to self-document the bottom row with one digit in each box. That is, the top row wasn't included in the count. The reason I bring this up is that your use of 12 seemed to rub me the wrong way (I like the idea of just single digits in each case). Whether such a solution exists for the Hofstadter variant (that is, where the top row is counted as well) is conditional on one of our programs finding the other solution.