Or by many worlds: the quarter is both ways in the box. When you each open your boxes, you yourself are pulled into the doubling. Now there are two pairs of you

Or by many worlds: the quarter is both ways in the box. When you each open your boxes, you yourself are pulled into the doubling. Now there are two pairs of you-and-them. In one pair, you hold heads and they hold tails. In the other pair, you hold tails and they hold heads. Thinking about this makes it clear how communication is impossible. You will always get both answers - for different values of "you".