You are not good at counting heads. In fact you are notoriously bad at it for somebody who has two math degrees. Here is what you should do next time: in addition to getting people to raise their hands, go around the room and ask them to state the next number in an easily-recognisable sequence, such as the natural numbers. Then use the sequence index to determine the number of heads. This is easy to verify because everybody knows whether they have been counted.
Also don't be such an idiot all the time. It's embarrassing.
P.S. Yes doing job interviews for jobs you aren't going to take is bad karma. I don't care whether you need the practice.
P.P.S. It's also bad karma not to let the library know of their security holes just so you can run PuTTY. Secure Shell is not worth eternal damnation.