Prolific puzzle inventor Henry Ernest Dudeney published the following problem in his 1917 book Amusements in Mathematics.The current version of the U.K.’s Union Jack flag was introduced in 1801. This image is a simplified version of the Union Jack that just consists of lines. Try to trace the lines with a pencil while only going through each line once. You should also lift the pencil from the paper and place it somewhere else as rarely as possible. Is it possible to draw the line version of the Union Jack in one go? If not, how many times do you have to reposition the pencil at minimum?
Spektrum der Wissenschaft, restyled by Amanda Montañez
You have to reposition the pencil seven times. The points where several lines meet are crucial for the solution: If you want to draw the design in one go, you have to move the pencil out of every point you draw into. So in order to be able to draw all the lines that meet at one point, the number of lines at that point must be even. Exception are the two points where you start and end the line. In the design there are 16 points with an odd number of lines, indicated in green, and 20 dots with an even number of lines, indicated in blue. The 16 green dots can be connected by eight green lines, with each point being either the start or end point. As a result, you have to move the pencil at least seven times while drawing.
And moving the pencil seven times is enough: Start at any green dot and draw the green line that extends from it. At the end of that you come to a green dot with two red lines. Choose one of them and then draw the entire red line without having to lift the pencil. You will end up at the green dot where you started drawing the red line. Now only the remaining seven green lines are missing, for which you have to pick up and put down the pencil seven times.
Spektrum der Wissenschaft, restyled by Amanda Montañez
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This puzzle originally appeared in Spektrum der Wissenschaft and was reproduced with permission.