To each his own.

Your analysis helps me realize that even as a kid, I was always more interested in the relationship between things than in the one and only solution to things. To me it hardly matters whether there are 0, 1, or many solutions to a problem. In the case of cryptosums, I'm fascinated by the fact that the mere arrangement and repetition of symbols provides enough information to deduce (a) whether or not a mapping between those symbols and the set of digits exists and (b) whether or not that mapping is unique.

How did you come up with those figures? According to this article, determining whether or not a solution even exists for a particular puzzle is NP-complete (if we allow for bases other than 10). Other than limiting the problem space to 10! possible mappings, how does limiting the problem to base 10 help one determine the potential number of puzzles with solutions, let alone the number of puzzles with unique solutions? Can you determine the number of problems without knowing exactly which particular puzzles will have solutions? Or did you use brute force to count the number of solutions for each puzzle?

Best, beth

Update: clarified question.