Then, continue your motion diagonally down and to the right, forming a roof on the box with your fingers. How can you draw a cross in a box without having to move your pen from the page?ĭraw a diagonal line from the top left corner of the box, which should be where the pen should be, towards the upper right corner of the box until you reach the midpoint of the box.
It consists of eight small squares, 18 single squares, nine 2 x 2 squares, four 3 x 3 squares, and one 4 × 4 square, all in different sizes. That’s right: it’s not the numbers 8, 16, 24, 28, or 30, and we’ll explain why later. The solution to the problem is 40 squares, which is the right answer. What is the total number of squares in this picture? With another way of putting it, there should either be NO odd nodes or precisely TWO odd nodes. This form can only be drawn without raising your pen or travelling over the same line again if the number of nodes with odd degrees is either zero or two, according to Euler’s theorem. Which figure can be drawn entirely without the use of a pencil? There were 22 related questions and answers found. Consider alternatives to the conventional wisdom. This is the 9-Dot Puzzle! Take a step back and look at the larger picture. Using just four straight lines, connect the nine dots together without raising your pencil from the page. How can you connect nine dots without raising a pen from the page? Give it a go right now, and then scroll down the page to get the answer. Each line must begin exactly where the previous line ended. Make a mark with your pencil anywhere on the paper and draw four straight lines without lifting your pencil from the page. You may practise this right now by rapidly drawing nine dots on a sheet of paper and then trying to solve the problem with a pencil. How can you solve the nine dots problem while keeping all of this in mind? The objective of the problem is to connect all nine dots with four straight lines or less, without raising the pen or sketching the same line more than once. Alternatively, fold the paper three times so that the rows of dots all line up, and then fold it again to allow the pencil to pass through!Īlso, do you know what the 9-dot puzzle is? Your goal is to connect all nine dots with just four (or less) straight lines, without taking your pencil from the page and without retracing the lines you have already drawn. Is it possible to connect all nine dots with four straight lines without lifting your pencil from the page in this situation? I haven’t been able to emulate this solution however the required folds can be viewed here.Using just four straight lines, connect the nine dots together without raising your pencil from the page. Below is a photo I took of this solution:Ī second one line solution involves origami and a specific placement and size of the dots on the page. The paper is then folded and a straight line is drawn connecting the dots.
The method I came up with when trying to solve this puzzle involved tearing the paper, not so much that any piece comes loose. There are several one line solutions to this puzzle. The three-line solution can be viewed below: There are rotations, reflections and variants to this solution: The one line solution requires that the paper be folded. Scroll down for a clue and further down for the answer.Ĭlue: The lines drawn are permitted to leave the area of the dots and continue on into the blank portion of the page in order to gain a better angle for subsequent lines. Printing the dots out or drawing them on paper is required for this solution. Rather than using 4 lines, can you solve it with 3 straight continuous lines?įinally, for anyone brave (or foolish enough) there is a more challenging further question that requires just 1 straight line to connect the 9 dots. There is a more challenging version of this puzzle. The task commonly posed is to draw 4 straight lines without taking your pen off the paper so that all 9 dots are joined. This well-known problem entails 9 dots as seen below.
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