13. Chiara has arranged 8 coins in a row. Some show the head side, others the cross side, in this sequence: TTTTTCCC. She plays this game: with each move, she chooses two consecutive coins and flips both of them. Chiara, with several moves of this type, wants to achieve a row of coins arranged in the sequence CCCCCCTT. What can be concluded?

(A) She can succeed with a minimum of 3 moves.

(B) She can succeed with a minimum of 5 moves.

(C) She can succeed with a minimum of 7 moves.

(D) She can succeed with an even number of moves.

(E) She cannot succeed.
(13) The correct answer is $(E)$.

Indeed, the number of $T$ in the sequence of coins remains always odd, after each move: therefore, it is not possible to reach a configuration containing exactly two $T$.

Question proposed by Gabriele Manganelli.