[Siegmund]

Others have already commented on the fact that the president may be better served by delegating the problem-solving to someone who excels at it, than attempting to solve all the problems himself. I still agree, in some sense, that I would like my president to have some kind of critical thinking abilities.

But mate in three (or two, or however many) problems are NOT the kind of situation they need experience with. In a mate-in-N problem, you are TOLD that the mate CAN BE DONE, and asked HOW. In some sense, it's mere lackey work, not executive work.
I would be a lot more interested in seeing potential presidents on their abilities to determine if something is possible in a deterministic game, or determine the line of pay with highest chance of success in a random game. The question for the country is "what is the way forward?" -- not "we know exactly where we can be in 3 years, how do we get there." Nobody is going to go to the president and say "A little bird told me that there's a way for you to talk North Korea into giving up its nukes if say the right three sentences to him. Figure out what they are."

Notice, too, that a mate-in-N problem is NOT the same thing as setting a goal - man on the moon in ten years, or whatever - lofty goals stated as "we will do this" still come with no guarantee that it is possible to achieve.