The answer to the coins puzzle:
The odds are 2 to 1 against being another head
Either you’re smart, or you guessed. In Planetarium, there are enough double-bluffs that you won’t get through if you rely only on guesswork. (And if you really did work it out, you won’t need to check the explanation).
This puzzle is just a warm-up.
It doesn’t form part of Planetarium itself.