To solve this you must know what is eulerian trail.......So get its info at https://www.youtube.com/watch?v=CQNH2ifOAQE
then tell me how you are gonna make a smallest eulerian trail, means the figure with least edges that makes it eulerian trail. Also tell me to which popular puzzle it is derived of and how......???
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The answer is IMPOSSIBLE.....
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READ QUESTION,,,,WHAT IMPOSSIBLE???????? :(
friends the smallest Eulerian trail is the smallest diagram drawn by 3 utility problem...... You can get more info at http://www.iosrjournals.org/iosr-jce/papers/Vol16-issue2/Version-10/C0162101322.pdf