  We show that all possible 388 4-dim Kochen-Specker (KS) (vector) sets (of
yes-no questions) with 18 through 23 vectors and 844 sets with 24 vectors all
with component values from \{-1,0,1\} can be obtained by stripping vectors off
a single system provided by Peres 20 years ago. In addition to them, we have
found a number of other KS sets with 22 through 24 vectors. We present the
algorithms we used and features we found, such as, for instance, that Peres'
24-24 KS set has altogether six critical KS subsets.
