# Walk on seven bridges with out walk on one twice (Koenigsberg) [duplicate]

How i can walk on these 7 bridges without walk on one of them twice?

After some research i found that "Koengsberg bridge" is not an Euler circuit.

• It's not possible... Oct 20, 2017 at 0:01
• @Ibrahim, if it isn't immediately obvious that the question we've marked this as a duplicate of is basically the same as this one, follow the "Seven Bridges of Koenigsberg" link in either the first comment under the question or GoodDeed's answer. Oct 20, 2017 at 0:41
• Since the question was "How i can walk on these 7 bridges without walk on one of them twice?", one of the solution is if you can swim(walk B-A-B-D-B-C-D, swim to A, walk A-C). Since you only said walk(not cross), you can walk B-A-B-D-B-C, walk halfway the C-A bridge, turn back in the middle, go back to C, walk C-D. Oct 20, 2017 at 8:03

I say it's impossible to walk on these 7 bridges without walk on one of them twice.

As the picture shows, each island has either 3 or 5 bridges connected to it, that's why I declare it impossible to walk on these 7 bridges without walk on one of them twice.

There's a proper proof out there that shows that: To walk on bridges only once each, EACH island must have an EVEN number of bridges connected to it. Or exactly 2 have an odd number of bridges connected.

Here, we have 4 islands having an odd number of bridges connected. So it's impossible to walk on these 7 bridges without walk on one of them twice.