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Limbic,
I've also got what I think is a perlygolfish approach. It's at least somewhat novel, even if implementation turns out to be impractical. I haven't implemented it at all, but I'll describe it here in the hope that it's interesting. Every number is either a factorial or the integer sqrt of some other number (well, actually, every number is the latter, but some are also the former). So when you look at a number, you check to see if it's a factorial. If so, you replace it with NF, where N is what you apply the factorial function to to get your number (that is, the inversefactorial of your number). Otherwise, you replace it with X..YS, where X and Y are the minimum and maximum values that you can plug into int(sqrt()) to get your number. S and F are literal characters to indicate the operation in your solution string. If you have already computed the solution for N, or for any number between X and Y, you can substitute that solution string for the number/range in your solution string and continue solving. Otherwise, you have to solve for it. If a factorial falls in your range, you replace your range with the factorial indicator as before. Otherwise, you expand your range using the inverse int(sqrt()) function. You proceed until the number (or range) at the beginning of your solution string includes your desired base case. Caution: Contents may have been coded under pressure. In reply to Re^2: Challenge: Chasing Knuth's Conjecture
by Roy Johnson

