6) In this rectangle there is exactly one false statement. In this rectangle there are exactly two false statements. In this rectangle there are at least three false statements. In this rectangle there are at most three false statements.

How many true statements are there in the rectangle?

$\begin{array}{lllll}\text { (A) } 0 & \text { (B) } 1 & \text { (C) } 2 & \text { (D) } 3 & \text { (E) } 4 .\end{array}$
6) The answer is (C). The first three statements contradict each other, so at most one of them can be true, which means there are at least two false statements, including the first one for sure. Furthermore, one of the last two statements must be true, and thus the fourth is certainly true. On the other hand, the fourth statement is compatible with each of the previous ones, which exhaust all the remaining possibilities: so one of them is also true.