Prize Box Puzzle

If you struggled to solve it, I recommend making a chart like this:

When Astrid says, “I know that Bill doesn’t know,” we know it cannot be a color that has a unique symbol. Green has a unique symbol (bolt), and so does purple (diamond). The winning box must not be green or purple, so we can cross out the green and purple rows. It must be blue or yellow.

When Bill says, “At first I didn’t know, but now I do,” we know it must be one of the remaining unique shapes. There are two clovers, so we can cross them out. We are left with heart (blue), star (yellow), or circle (yellow.)

When Astrid says, “Then I also know,” it tells us the box must be blue. If it were yellow, she couldn’t know, because it could be either the yellow star or the yellow circle. This means the winning box is the blue heart.