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Nine dots and four dashes


There are nine points on a square grid. Can you connect these dots with four straight lines without lifting the pen?



You probably know the game »The House of Santa Claus«.

The task is to draw the eight-line house in such a way that the pen always stays on the paper.

The following problem is similar.

There are nine points arranged on a square grid - see sketch above.

You should connect these nine dots with four straight lines without lifting the pen.

Can you do it?

There is an additional question: Is it possible to connect the nine dots with three dashes?

If not, why not?

The sketch below shows the required solution for four lines.

You can start drawing in two places: either at the bottom right corner or at the end of the line at the top left.

The task cannot actually be solved with three lines.

The way the points are arranged, there are no more than three points on a straight line.

With only three dashes, we would have to hit three points with each dash.

It works with the first stroke - but it's no longer possible with the second stroke.

Either because the next three points can only be reached by a line running parallel to the first dash.

Or, if the first line runs diagonally, because there are no three more free points that lie on a line.

However, there is a solution that gets by with three lines.

This takes advantage of the fact that the points in the drawing are small circles and not points with zero area.

If we do not draw the lines exactly through the center of these circles, the nine points can be connected in three moves - see the following drawing.

I discovered this riddle in Heinrich Hemme's book »222 Knobeleien for every occasion«.

It dates back to puzzle writer Sam Loyd.

In case you missed a mystery from the past few weeks, here are the most recent episodes:

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Source: spiegel

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