Question

You've lost your dinner jacket in a palace with 1,514 doors, and it could be anywhere. how many rooms must you potentially look through to find it?

Answer 1

Presuming the rooms are connected to each other by a door and that each room has two doors, you will potentially check in;
$\frac{1514}{2} -1$
= 756 rooms
We are subtracting 1 since the last door doesn't lead to another room.