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We apologize for your futile efforts in trying to solve the problem. In fact, Euler proved that no solution exists. It is easy to see why. The four land masses are the north and south shores and the two islands. Any path must arrive at and depart from a land mass via two different bridges (lest one bridge be used twice), so for any legal path to exist, each land mass must be approachable by an even number of bridges.

Euler's more sophisticated treatment can be considered as the beginning of what is now graph theory and, more generally, the entire field of topology.

Snapshot 1: an illegal solution since one bridge is crossed twice

Snapshot 2: adding an eighth bridge can make the problem solvable

Snapshot 3: with two of the bridges destroyed by bombing in World War II, another solution is possible

Reference

[1] Wikipedia. "Seven Bridges of Königsberg." (Jul 8, 2013) en.wikipedia.org/wiki/Seven_Bridges_of _K % C3 % B6nigsberg.