I'd like to say too many to count. A lot of instances I was able to figure out the answer by remembering that said answer was shown in the preview at the end of the previous episode, though does that count strictly speaking?
Unless its something obvious, no, because the idea is no summary, no preview mention, but I guess if its staring in your face, sure.
There hasn't been a lot of instances in this series where the answer can only be figured out by watching that episode specifically. (One such example being the pancake race in SM013)
What I mean is some of the Poke problems have been (at least similar maybe not exact):
Where does the setting of this episode take place?
Who visits Ash at Kukui's house?
What happens to such and such.
And at least for the first example, that COULD easily be answered in the first few seconds "Our heroes journey to Ula'Ula island"
Oh, okay that was one of the options, well Poke problem solved.
But this one is especially weird because the answer was revealed the previous episode, so it creates a weird logic issue, where you are like "Wait, are they doing the finals in this episode, starting, anyway, is that why you are asking?" only to watch the episode and then you're like "Oh no it was what I thought to begin with, great, thank you, we already knew who it was."
I'm sure the Poke problems are most definitely for kids, but honestly I don't know why they chose one that make it seem like children have amnesia of the previous episode.
Just think maybe a more relevant question to the episode rather than connected directly from the previous episode, is what the Poke problems should be about. But whatever just found it strange, they asked a question you already know from watching the previous episode.