What is the largest number of the following statements that can be true at the same time?
I) $0 < x^2 < 1$
II) $x^2 > 1$
III) $-1 < x < 0$
IV) $ 0 < x < 1$
V) $0 < x - x^2 < 1$
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
This problem is taken from the UKMT Mathematical Challenges.