Example of finite simply connected space

Is there any space with such properties? If there is no such space, I would be very grateful if you could tell me proof of this fact.

-
Er...any singleton? –  DonAntonio Mar 25 '13 at 15:02

EDIT: It is "easy" to construct examples of simply-connected non-contractible spaces. An easy one is the space associated to the poset $P=\{(a,b): a=0,1; b=0,1,2\}$ where $(a,b)<(a',b')$ if $b<b'$ (this is a model of $S^2$).