I wonder if calling those two separate “systems” is an artificial divide. At least some of the fast, instinctive judgments we make come from previous experience, perhaps originally performed slowly and analytically. So things can drift from “2” to “1” as we learn to respond reflexively to patterns.
I still is it’s fascinating, especially in how we’re fooled: when do we falsely match a pattern (as in the math questions above), or what intuitive judgments of ours have no basis at all in experiential or analytical thinking?