history of the ripe Dot problem

The ripe dot difficulty is a classic lateral thinking exercise that obtained widespread popularity in the 1970"s and 80"s. Participants room presented v a collection of dots arranged in a 3x3 grid and challenged to connect all nine dots, without lifting their pencil indigenous the paper, using the fewest possible variety of straight lines. 

Copy the straightforward diagram below onto a piece of document and give the puzzle a try for yourself before reading any kind of further.

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The solution calls for one come "think external the box" and while some complete that the nine dot trouble served as the impetus for this famous turn that phrase, others point to a cognitive performance test indigenous 1945 known as Duncker"s candle problem. 

In Duncker"s test, participants are presented v a candle, a book of matches and also a box full of press pins. The difficulty is to affix the candle to the wall surface in together a means that when the candle is lit, the wax will not drip ~ above the table... The solution needs the practical use of the box which at first, might seem come be included simply come contain the push pins. 

Whether or not the nine dot problem is in truth the initial inspiration for the cliched metaphor, the puzzle itself definitely pre-dates the phrase. The an initial known publication remained in Sam Loyd"s classic Cyclopedia of Puzzles, 1914.


Though, in a 1959 compendium of Sam Loyd"s work, young name Gardner defined this certain puzzle as a "classic geometrical challenge" so the nine dots likely predate Loyd"s eggs. The enduring element of the puzzle is the it highlights the means our minds tend come impose unnecessary limitations upon approaches of attack problems. For those unfamiliar, the most renowned solution to the puzzle is illustrated below.


Clearly, this solution needs one come "think outside" the "box" the is developed by the nine dots yet if we room to completely embrace the idea the "outside the box" thinking, why stop there? Here"s a method to settle the puzzle using only three right lines.


This systems is also further "outside the box" 보다 the first. Yet what if the box is no the square explained by the nine dots but rather, the item of document the puzzle is published on? If we think external of the box, the is possible to fix the puzzle using only one straight line. 


Even there is no manipulating the paper, there is still another means to resolve the puzzle using only one straight line.

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Of course, the heat is so lengthy that it circles the planet twice but that is directly nonetheless and solves the puzzle successfully. So perhaps the biggest lesson the the nine dot problem is no to "think outside the box" however rather, that as soon as it involves truly creative problem solving, there is no box.