Nine cards, each uniquely marked with a single-digit from 1 to 9, are randomly dealt to three players, each player receiving three cards. Every player sees his own cards, but is unaware of the cards in other players' hands.

Each player declares the sum of the three cards in his own hands. Based upon this information, the players try to guess the cards in their opponents' hands.

Imagine players A, B, and C play this game, and the following conversation ensues:

A: The sum of my cards is 14.

B: The sum of my cards is 15.

C. The sum of my cards, obviously, is 16.

A. I can't guess any card in B's hand.

B. I can't guess any card in C's hand.

C. I know the cards in everyone's hands.

What are the cards in player B's hand? Explain your reasoning.

Each player declares the sum of the three cards in his own hands. Based upon this information, the players try to guess the cards in their opponents' hands.

Imagine players A, B, and C play this game, and the following conversation ensues:

A: The sum of my cards is 14.

B: The sum of my cards is 15.

C. The sum of my cards, obviously, is 16.

A. I can't guess any card in B's hand.

B. I can't guess any card in C's hand.

C. I know the cards in everyone's hands.

What are the cards in player B's hand? Explain your reasoning.