Name: Anonymous 2007-11-16 22:51
that shows that this is impossible to solve?
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The above was a puzzle I spotted in /b/. The instructions were to draw the image you see on a sheet of paper and using one continuous line, without crossing itself or the same line segment twice, pass through all 16 segments at least once. I believe it is impossible - is math available to prove me right?
The top half of the box, to be solved in the same manner as the puzzle, requires 7 segments to be crossed (since the two boxes share a common side). The lower half requires 10 segments to be crossed (since the middle box shares two of the would-be 12) giving us a total of 17 segments to cross IN ORDER to solve using one unbroken, uncrossed line, however there are only 16 segments available for the whole puzzle.
On any 15th move there is one unreachable segment left, so essentially you must use the 16th "move" to cross a segment twice, and the 17th move is the one which would complete the puzzle - illegally.
Is there anything you all would add to this or disagree with? I'd like to see a simple math solution as to why this won't work. Thanks for your assistance.
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The above was a puzzle I spotted in /b/. The instructions were to draw the image you see on a sheet of paper and using one continuous line, without crossing itself or the same line segment twice, pass through all 16 segments at least once. I believe it is impossible - is math available to prove me right?
The top half of the box, to be solved in the same manner as the puzzle, requires 7 segments to be crossed (since the two boxes share a common side). The lower half requires 10 segments to be crossed (since the middle box shares two of the would-be 12) giving us a total of 17 segments to cross IN ORDER to solve using one unbroken, uncrossed line, however there are only 16 segments available for the whole puzzle.
On any 15th move there is one unreachable segment left, so essentially you must use the 16th "move" to cross a segment twice, and the 17th move is the one which would complete the puzzle - illegally.
Is there anything you all would add to this or disagree with? I'd like to see a simple math solution as to why this won't work. Thanks for your assistance.