The World of Work
An inspector had to inspect 6 buildings at the corners of a 2 by 1 section of rectangular grid. Starting from the building in the lower left hand corner and walking only along the rectangular grid lines that mark out the city blocks, how many ways can he do this without walking along the same block twice?
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1 solution
Moderator note:
Those are 3 possible ways. You have not established that no other way is possible.
He can loop around the perimeter in either direction, or he can go lower left -- upper left -- upper middle -- lower middle -- lower right -- upper right. That's 2 + 1 = 3 ways.