9/10/2023 0 Comments 3 lines 4 dots![]() It is also possible to fold the paper flat, or to cut the paper into pieces and rearrange it, in such a way that the nine dots lie on a single line in the plane. Thus a single line can be drawn connecting all nine dots-which would appear as three lines in parallel on the paper, when flattened out. Īnother way to use only a single line involves rolling the paper into a three-dimensional cylinder, so that the dots align along a single helix (which, as a geodesic of the cylinder, could be considered to be in some sense a straight line). Or, if the line is allowed to be arbitrarily thick, then one line can cover all of the points. If the dots are assumed to have some finite size, rather than to be infinitesimally-small mathematical grid points, then it is possible to connect them with only three slightly-slanted lines. Various published solutions break the implicit rules of the puzzle in order to achieve a solution with even fewer than four lines. The inherent difficulty of the puzzle has been studied in experimental psychology. According to Daniel Kies, the puzzle seems hard because we commonly imagine a boundary around the edge of the dot array. The phrase thinking outside the box, used by management consultants in the 1970s and 1980s, is a restatement of the solution strategy. To do so, one goes outside the confines of the square area defined by the nine dots themselves. It is possible to mark off the nine dots in four lines. Solution One solution of the nine dots puzzle. In the 1941 compilation The Puzzle-Mine: Puzzles Collected from the Works of the Late Henry Ernest Dudeney, the puzzle is attributed to Dudeney himself and not Loyd. Sam Loyd's naming of the puzzle is an allusion to the story of Egg of Columbus. King Puzzlepate performs the feat in six strokes, but from Tommy's expression we take it to be a very stupid answer, so we expect our clever puzzlists to do better The puzzle is therein explained as follows: The funny old King is now trying to work out a second puzzle, which is to draw a continuous line through the center of all of the eggs so as to mark them off in the fewest number of strokes. In 1914, Sam Loyd's Cyclopedia of Puzzles is published posthumously by his son (also named Sam Loyd). Christopher Columbus' Egg Puzzle in Sam Loyd's Cyclopedia of Puzzles, 1914 From at least 1910, Pearson's "nine dots"-version appeared in puzzle sections. From at least 1908, Loyd's egg-version ran as advertising for Elgin Creamery Co in Washington, DC., renamed to The Elgin Creamery Egg Puzzle. īoth versions of the puzzle thereafter appeared in newspapers. It was there named a charming puzzle and involved nine dots. In the same year, the puzzle also appeared in A. The lines may pass through one egg twice and may cross. The problem is to draw straight lines to connect these eggs in the smallest possible number of strokes. In 1907, the nine dots puzzle appears in an interview with Sam Loyd in The Strand Magazine: " Suddenly a puzzle came into my mind and I sketched it for him. The Columbus Egg Puzzle from The Strand Magazine, 1907 Said chess puzzle corresponds to a "64 dots puzzle", i.e., marking all dots of an 8-by-8 square lattice, with an added constraint. In 1867, in the French chess journal Le Sphinx, an intellectual precursor to the nine dots puzzle appeared credited to Sam Loyd. The puzzle has appeared under various other names over the years. ![]() The nine dots puzzle is a mathematical puzzle whose task is to connect nine squarely arranged points with a pen by four (or fewer) straight lines without lifting the pen. The puzzle asks to link all nine dots using four straight lines or fewer, without lifting the pen. ![]() Mathematical puzzle The "nine dots" puzzle. ![]()
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