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Five room puzzle
This classical,〔 Gardner titles the problem (puzzle) as "Cross the Network" and refers to it as one of the oldest of topological puzzles.〕 popular puzzle involves a large rectangle divided into five "rooms". The object of the puzzle is to cross each "wall" of the diagram with a continuous line only once.〔According to "One often encounters Eulerian graphs as puzzles. Consider the famous floor plan that consists of five rooms interconnected with themselves and the outside by doors on every wall. The puzzle is to start in one room or the outside, walk through every doorway exactly once, and return to the starting point."〕
==Solutions==
As with the Seven Bridges of Königsberg, the puzzle may be represented in graphical form with each room corresponding to a vertex (including the outside area as a room) and two vertices joined by an edge if the rooms have a common wall. The resulting multigraph does not contain an Eulerian path nor an Eulerian circuit, which means that this puzzle cannot be solved. Solutions missing one wall, however, are possible (see image).
By bending the rules, a related puzzle could be solved. For instance, by permitting passage through more than one wall at a time (that is, through a corner of a room), or by solving the puzzle on a torus (doughnut) instead of a flat plane.
(note the uncrossed wall – marked with circle)
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
■ウィキペディアで「Five room puzzle」の詳細全文を読む
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