The value of $$k$$ for which the equation $$x^3 - 6x^2+11x+(6-k)=0$$ has exactly three positive integer solutions is ------.

For integer roots summing to $$6$$ with pairwise-product sum $$11$$, the only positive integer triple is $$1, 2, 3$$, since $$1+2+3=6$$ and $$1\cdot2+2\cdot3+3\cdot1=11$$. Comparing with Vieta's formulas, the product of roots is $$k-6$$, and $$1\times2\times3=6$$, so $$k=12$$.