19. Consider the equation $a x^{2}-b x+a=0$ in the unknown $x$, where $a$ and $b$ are positive real numbers. Among the following 5 statements, how many are true?

- If $b>2 a$, there are two distinct real solutions.
- If there are two distinct real solutions, they are positive.
- If one of the solutions is 9 times the other, then $b>3 a$.
- No matter what $a$ and $b$ are, there cannot be two distinct integer solutions.
- If there are two real solutions, their product is 1.
(A) only 1
(B) 2
(C) 3
(D) 4
(E) all 5
(19) The correct answer is $(A)$.

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

(Question proposed by G. Manganelli)