orientability of surface and odd/even no. of punctures

Question

Suppose that T is a surface with Euler characteristic -4.

1. Is it orientable or non-orientable?
2. Does it have odd or even number of punctures (disks)?

Answer 1

If $d=1$ or $d=3$ or $d=5$ then $T$ is non-orientable, as $p$ must be odd.

If $d=6$ then $T$ must be orientable, as $p=0$.

If $d=4$ we can have $t=1,p=0$ orientable or $t=0,p=2$ non-orientable.

If $d=2$ then $T$ can be either, as we could have $t=2,p=0$ orientable or $t=1,p=2 $ or $t=0,p=4$ both non-orientable.

Finally if $d=0$ we could have $t=3,p=0$ orientable, or $t=0,1,2$ all non-orientable.

There isn't really anything else you can say with the given information.