Hi there! The bridge will appear when one switch has been pulled however not when a certain one is pulled.
Bridge =< 1, switch 1=+1, switch 2=+1, switch 3 =-1, switch 4=+1
So long as the number is greater than one the bridge to the larger part of the room will appear, however you need to make the switches equal 3 for the crystal to light up and the final "small door" to open. Hope that helps!