What do you get after connecting the dots? Therefore, focus on depicting form, not on drawing lines. Lines describe the edges of the forms that we see. So, to draw accurately, THINK FORM, not line. You draw it by starting at a vertex of odd degree (or anywhere in case there are none.) Can you draw a form without a line? Whether the graph is bipartite or not has no effect. There is an Euler path in a connected graph if and only if the number of vertices of odd degree is 0 or 2. Can you draw a graph without lifting your pen? In graph theory, the number of odd degree vertices should only be 0 or 2, then you can draw this graph without lifting pen off paper, and it must start from one odd degree vertex and end at the other one if it has 2 odd degree vertices. Can you draw a diagram without lifting the pen square with diagonals? The origins of the phrase “thinking outside the box” are obscure but it was popularized in part because of a nine-dot puzzle, which John Adair claims to have introduced in 1969. To switch between apps, click the app launcher icon, then select an app. Microsoft calls this the “nav bar.” The icon at the far left (nine dots) is the app launcher, where you can access the various parts of Office 365, including Outlook mail, calendar, people, OneDrive, Office Online apps, and more. The nine-dot problem (Maier, 1930) requires that nine dots arranged in a square be connected by four straight lines drawn without lifting the pen from the paper and without retracing any lines (Figure 1). It’s easy to demonstrate the knight’s-move if you do it slowly - just stay away from the dark disk around each nearby dot. The number of patterns available becomes 766752. How many patterns are possible with 9 dots? The solution lies in the observation that it’s permissible to cross square boundaries. For one always comes up with 5 lines instead of 4. The 9 Dots Problem The problem is to connect the dots with no more than 4 straight lines without lifting your hand from the paper. A curve can be drawn without lifting a pen or pencil as we are joining different points that satisfy the curve. Plane curve: Plane curve means a curve (not a straight line) that lies in the plane and can be closed or open. Which figure can be drawn without lifting the pencil? Most people will see a square and mentally add lines around it creating the context with which to solve the puzzle. The rules are simple connect all 9 dots using a maximum of 4 straight lines without lifting your pen off the paper or retracing back over an existing line. you must not lift your pen from the paper once you start drawing. The straight lines must be continuous – i.e. To solve the problem, you need to join all nine dots by drawing no more than four straight lines. Can you join 9 dots with four straight lines without taking your pencil off the paper you can not go over any line? From this point, you lead the next line to the last dot of the second column and then to the second dot of the third column. Here are some related question people asked in various search engines.ĭraw a straight line down from the very first dot (in other words, draw a left side of the square), but make it a bit longer, as if there was the fourth dot below Step 2.
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