We received three good solutions - two almost completely correct,
fromYanqing from Lipson Community College and from Sarah from Colyton, and
one completely correct from Andrei from Tudor Vianu College in Bucharest.
Well done to you all.
Andrei's solution follows:
First, I observe that for the first figure it is impossible to cross each
bridge once. This happens because you would remain in a place where all
the bridges were already crossed.
In the second case, it is
possible to cross the bridges only once and create a circuit.
worked with different number of bridges and islands and I obtained
solutions for each of the following:
- bridge traversing circuits
- bridge traversing paths
- Hamiltonian circuits
- Situations where
none of the above is possible.
For 8 bridges I found:
- A diagram with a bridge traversing circuit.
The circuit is the following: S-C-A-D-B-A-C-B-S
- A diagram
with a bridge traversing path:
The path is the following: S-D-E-A-B-S-C-E-B.
- A Hamiltonian
circuit and a bridge traversing circuit:
- A diagram in which neither is possible. In the diagram below, neither a
traversing path nor a traversing circuit is possible:
If you were allowed to start at another island you could
have a traversable path: starting at the top right hand island and
finishing in the top left hand island, or vice versa.