The problem is really simple, but I have absolutely no idea on how to solve it.
So there is an ant who really wants to get to the other side of a grid shaped bridge. However, a person decides to stop the ant from crossing over, so he gets a coin and starts throwing it for each of the 28 black line segments.
If the coin that he threw is a tail, he cuts out that line segment, and if the coin that he threw is a head, he leaves the line segment alone.
After he does this for every 28 black line segment, what is the possibility that the ant still can cross the bridge?
Consider the dual ant that tries to get from one green line to the other across the gray bridge:
Exactly one of the ants can cross. By symmetry, the probability for either to be able to cross is $\frac12$.