Sketch skipping the OPEN Arduino inputs
You should always connect something to an input to pull it high or low when no signal is present.  The simplest thing is to activate the built-in pullup resistor, which will result in the input returning HIGH when there is nothing connected.  If that's not compatible with your particular use, add a resistor from the input to ground (10k-100k is fine) so that it will return LOW when nothing else is connected.  If the input is just floating, it is susceptible to noise causing random state changes. The input impedance is very high (100 Meg) so it can pick up static and other mischief.