The answer to the coins puzzle:
Not 50/50
The odds are 2 to 1 against.
You’re going to have to sharpen those wits if you want to keep up. There’s an explanation if you want to know why you’re wrong . . . but in the meantime, take our advice and don’t bet with mathemagicians.
This puzzle is just a warm-up.
It doesn’t form part of Planetarium itself.