A group of shapes, all with lines leading to their center point. The shapes are a triangle, square, pentagon, hexagon, octagon, and decagon. The image above shows a group of shapes, all with lines leading to their center point. These shapes cannot be drawn with the following rules:

  1. You may not trace over over an already existing line.
  2. You may only draw lines that are part of the shape.
  3. You may not move your writing utensil while it is up and you are drawing this shape.

This can be done within shape, not just the above. Why is this?

  • 2
    $\begingroup$ Graph theory 101. $\endgroup$ Jul 13, 2016 at 19:25
  • 1
    $\begingroup$ Not a hard/good puzzle, but a very valid question for somebody honestly seeking reasons and explanations. I don t think it deserves DV just because it is easy to answer, as this is a WHY question, not a 'Solve my challenge' puzzle. $\endgroup$
    – BmyGuest
    Jul 13, 2016 at 19:56
  • $\begingroup$ @BoxTechy When you think a posting answerd your questions, it would be courtesy to 'accept' the according answer with the little checkbox item under the voting buttons. $\endgroup$
    – BmyGuest
    Jul 13, 2016 at 21:32
  • $\begingroup$ Essentially a duplicate of Drawing something using one pen stroke. $\endgroup$ Jul 28, 2016 at 10:52

1 Answer 1


This is a variation of the Seven Bridges of Königsberg puzzle.

The answer is you can't trace out the pattern if more than two nodes are odd. We call a node "odd" if it has an odd number of lines to it, and "even" if an even number. (If a node is not an endpoint of the drawn line, then the drawn line must enter that node the same number of times as it leaves it, so the node must be even. So the only nodes that can be odd are the endpoints of the drawn line. Because a single line has two endpoints, a beginning and an end, more than 2 odd nodes would indicate more than 2 endpoints.)

  • $\begingroup$ You have a typo -- "if more than two nodes ..." should be "if no more than two nodes". $\endgroup$
    – Gareth McCaughan
    Jul 13, 2016 at 18:52
  • 1
    $\begingroup$ @GarethMcCaughan fixed. $\endgroup$
    – Jiminion
    Jul 13, 2016 at 20:03

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