Are you primed for homework?
As a simple substitution problem, there are only 9 letters in the puzzle and 10 digits to choose from. We know that 0 must be one of the numbers in play.
As explained in the comic, we know that three of the letters must represent 9, 1, and 0. That leaves a number of possibilities for D and N which must add up to 9.
This is where the "meta-puzzle" comes in. If we ignore the actual words, there are 8 possibilities that can be found using 7 & 2, 2 & 7, 3 & 6, and 6 & 3. If you use 4 & 5, then you will have to repeat a digit.
If, according to the meta-puzzle, ODD must be odd, then D must be 7 or 3. (Again, 5 won't work, but feel free to try it.)
These now have four solutions because "O" and "V" will be interchangeable. That is, there is nothing to prevent you from switching those two place values.
Of these four solutions, there will actually be only two distinct totals (because switching O and V doesn't affect its sum). Of those two, one will be a prime number and one will not. There will be an easy divisibility test to see which one is composite.
A big Thank You has to go to Rebecca Rappaport and her math-a-day calendar, where this puzzle came from. In that puzzle, you were asked for the sum of P + R + E, which is 1 + 0 + 9 = 10. This puzzle appeared yesterday on the tenth. I wrote the "official" solution, which didn't require a full solution, but I wanted to do one anyway. I didn't take the ODDness or EVENess or PRIMEness into account when I mentioned 8 solutions.
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