My mom is 52 years old and she remembers when she was a kid, her brother showed her how to solve this puzzle. But she forgot, and for the last 40 years she has been trying it but has always failed. See if you can help. Puzzle: Draw a horrizontal rectangle. Now, draw a line in the middle of the rectangle horrizontally. Now on the top half, draw a vertical line in the middle. On the bottom half, draw 2 vertical lines on each side of the top line. Kind of like this l l l But inside of the rectangle. Draw a continuous line that goes through each line segment one time only. She now believes it is mathematically impossible. Can you do it?
oops, my diagram didnt turn out right. But yes you can curve it. Just don't cross over a line segment twce. So there is a total of 16 line segments.
It's mathematically impossible. There are some sites out there that explain why. Your mom's off her rocker.
Short answer as to why it's impossible: Because there are more than two vertices with an odd number of edges connecting of them. (In this case, there are eight.) If she can handle some math and a bunch of hyperlinks, try here: http://mathworld.wolfram.com/EulerianTrail.html
lol. nice link. She doesn't need any maths. This problem doesn't even involve multiplications ( which I consider advanced maths already ) All it needs to know is what's even and what's odd. And this particular puzzle is a variant of the original problem. i.e draw a curve across the edges is equivalent to actually draw the edges (and therefore vertices)
tell her to try this one: draw a rectangle horizontally. then draw 2 more horizontal lines within the rectangle leaving equal space. then, draw three vertical lines within the rectangle within equal space. you should end up with 12 equal boxes. then, "X" out the 4 corner boxes. with the 8 remaining boxes, use the numbers 1 - 8 to fill them in. the trick is to fill in the boxes without having adjacent numbers touching each other. for instance, 1 and 2 cannot have a common border OR corner. neither can 2 and 3, 3 and 4, and so forth.
EDIT: I take it all back. I guess technically by retracing the same line, you cross a segment twice, so my idea didn't work out after all.
Do you have to stay inside the rectangle or can your lines extend outside the drawing? There is a puzzle in which you have the following diagram: . . . . . . . . . The quest is to not remove your pencil from the paper and draw 4 lines which go through all 9 dots. You can cross an existing line. The answer involves "thinking outside the box".
