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#9 dots 4 lines brain teaser how to#
#9 dots 4 lines brain teaser trial#

Second property: All joining lines are to be drawn on a plane surface.

We cannot use this property for solution-obviously we must use straight lines.

First property: A joining line must be straight.

Let us list out the properties of our main entity, the joining line. If the obstacle could solely be fixed by adjusting this overlooked attribute, the problem will prove impossible to solve. As a result, choice of considering the invisible property is overlooked. When a problem demands out-of-the-box idea to fix, usually an attribute of the primary entity in the obstacle (in our problem, a joining line) remains invisible. Attribute analysis of connections to identify taken-for-granted attribute: Connect the nine dots riddle So obvious ways of joining the dots cannot give you the solution. Total number of lines is now 6, again an invalid solution.

#9 dots 4 lines brain teaser trial#

Let us complete this second trial by joining the rest 4 dots in a simple way.

#9 dots 4 lines brain teaser how to#

Point is, how to connect the remaining 4 dots and join the resulting lines with the two existing lines? Where should the joining pencil move after joining three diagonally placed dots?Ĭonclusion 5: It can only be along one of the two adjoining mutually perpendicular outer boundary sides of the grid.Ĭonclusion 6: The two lines, one diagonal and the other a vertical line, together join 5 dots and this combination must be a part of the final solution. It is identified that the most efficient oblique line joins three dots,Ĭonclusion 4: One primary line in the solution must be one of the two diagonals. Solution to connect the nine dots riddle: Second trial and analysis of its results To try out the new ideas, we need a second experiment. All 5 lines in the figure are directed vertically or horizontally with no oblique line.Ĭonclusion 3: Whichever way you join the dots with these mutually perpendicular sets of lines aligned with the two axes, solution cannot be reached. Observation: A property of the connections not considered is the direction of the lines. Number of secondary lines should be least. In the trial, we used 3 primary lines and two secondary lines.Ĭonclusion 2: Secondary lines do not contribute to joining more dots and so are wasteful. The joining is invalid with 5 straight lines.Ĭonclusion 1: Two groups of lines to analyze-primary lines joining the dots and lines joining the primary lines. But to connect the 3 lines, 2 more straight lines are used. Observation: To connect the nine dots, three independent straight lines each joining 3 dots are used. What clues can we get from this simple trial? Solution to connect the nine dots riddle: first trial and analysisĪs a first trial, the nine dots are joined in the simplest manner violating no condition. To solve, you may choose either trial and error or systematic reasoning.Īs trial and error is arbitrary with no certainty of result within a reasonable time, it is rejected.įirst step in any serious problem-solving is to make a quick trial, analyze the results of the trial and make a key conclusion. Soon you figure out that the puzzle is hard. Solution to Connect the nine dots riddle: Analysis and strategy decision Hint: The puzzle is hard and demands out-of-the-box thinking. The nine dots in a 3-by-3 two-axis grid shown.

Join the nine dots in a 3-by-3 two-axis grid by 4 straight lines without visiting a dot more than once and without raising your pencil from the paper. Learn how to solve the tough puzzle from the solution. Join the nine dots in a 3-by-3 grid by 4 straight lines without raising the pencil.