I asked my students the following questions in class. We've covered outcome classes, but are not quite at game values yet.
Let X be the Domineering position that is two empty squares tall.
Let Y be the Domineering position that is four empty squares tall.
Find a Domineering position, G, such that X + G is in P (Zero) but Y + G is in L (Positive)
That one's not too tough. Neither is the next one:
Find G such that X + G is in R (Negative) but Y + G is in P.
This one's nice:
Find G such that X + G is in N (Fuzzy) but Y + G is in L.
My first solution for this one had a composite (sum) game for G, but I've since found a non-composite solution:
Find G such that X + G is in R, but Y + G is in L.
If you know a bunch about the values of Domineering positions, I guess these are relatively simple. If not (or if you are good at forgetting), perhaps they require a bit of extra time to consider.
1 day ago