The Five Rooms

five rooms

Here’s the floor plan of a house with five rooms. Can you draw a continuous line that passes through each of the 16 wall segments once and once only? If it’s possible, show how; if it’s not, explain why.

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It’s impossible. Three of the rooms have five wall segments, an odd number. A continuous line that starts outside such a room and crosses all five wall segments will be “trapped” inside the room, with no way to exit. We can start the line in one five-walled room and end it in another, but the third presents an insoluble problem. See The Bridges of Konigsberg and Knotty Thinking.

June 9, 2012February 4, 2013 | Puzzles